Matt Rognlie on secular stagnation

In the comments of Askblog, Matt writes:

…the “secular stagnation” hypothesis is in dire need of some cogent back-of-the-envelope estimates, and I don’t think it holds up very well. A long-term fall in the average real interest rate from, say, 2% to -1%, would be absolutely extraordinary. It would imply massive increases in the valuation of long-lived, inelastically supplied assets like land, and massive increases in the quantity of long-lived, elastically supplied capital like structures.

Just to illustrate how extreme the implications can be, consider the following (sloppy) calculation. The BEA’s average depreciation rate for private structures is currently about 2.5%. A decline in the real interest rate from 2% to -1% implies a decline in user cost r+delta from 4.5% to 1.5%, of a factor of three. If the demand for structures is unit elastic (as economists, unjustifiably from an empirical standpoint, tend to assume with Cobb-Douglas functional forms), this would imply a threefold increase in the steady-state quantity. Since structures are already 175% of GDP, this would imply an additional increase of 350% of GDP, more than doubling the overall private capital stock and nearly doubling national net worth. The transition to this level would require such an extraordinary, prolonged investment boom that we would not face slack demand for many, many years.

(There are many things wrong with this calculation, but even an effect a fraction of this size serves my point, especially when you keep in mind that land values would be skyrocketing as well. The bottom line is that proponents of secular stagnation have not yet contended with some of the basic numbers.)

There is more here.  That is via David Beckworth.

I am still waiting for a model of secular stagnation that rationalizes both a negative real interest rate and positive investment, which indeed we are observing in most countries circa 2014.  That means, by the way, I don’t quite agree with Matt’s sentence “The transition to this level would require such an extraordinary, prolonged investment boom that we would not face slack demand for many, many years.”  There are some “reasoning from a price change” issues floating around in the background here.  Is it the productivity of just new capital that has fallen to bring the natural interest rate to negative one?  Or the rate of return on old capital too, in which case the value of the extant capital stock is not given by the calculation in question?  Tough stuff, but you know where the burden of proof lies.  Can this all fit together with the fact that nominal gdp is now well above its pre-crash peak?  And that we are seeing positive net investment?  In any case I agree with Matt’s broader point that the implied magnitudes here don’t seem to fit the facts or even to come close.

Speaking of Piketty (or did I mean to write “speaking of Scott Sumner?”), Scott has a question:

…here’s what confuses me.  Some of the reviews seem to imply that Piketty argues that real rate of return on capital represents the rate at which the wealth of the upper classes grow.  Is that right?  If so, what is the basis of that argument?  I don’t think anyone seriously expects the grandchildren of a Bill Gates or a Warren Buffett to be 10 times as wealthy as they are.


not read it yet but Eggertsson and Mehrotra's new paper "A Model of Secular Stagnation" is supposed to be good: See blog review:

Yet it has no capita in the model, and it cannot generate positive net investment. This is telling.

E&M have an interesting start, but yes the big flaw is no capital, and that seems to be the assumption of everyone on the blogosphere as well, as if investment is not part of aggregate demand. E&M also assume an exogenous borrowing constraint, which I find somewhat less problematic but still assumes the result to some degree.

They say that they will be adding capital to the model and expect the results to hold. I will be very interested to see how they do that; they'll need some sort of barrier to investment.

Ryan and Tyler:

Can you further explain why the absence of capital in the model is a big deal? Thanks.

'I don’t think anyone seriously expects the grandchildren of a Bill Gates or a Warren Buffett to be 10 times as wealthy as they are.'

In a similar vein, I'm confident that the grandparents of both Bill Gates and Warren Buffett never expected any of their grandchildren to be billionaires.

And yet, welcome to what happened, compared to what one predicts.

Yes, I found that a curiously circular comment. Did I miss something? It sounds like he just said X probably won't happen because nobody thinks X will happen.

Someone wins a lottery. Do you expect their grandchildren will too?

Alternatively, someone does not win the lottery. Do you expect their grandchildren will not win either?

That analogy works only if you think life is a random walk. Do you think it was just dumb luck that made Bill Gates a billionaire?

Individual fortunes obviously vary greatly, but Piketty argues persuasively that inheritance is increasingly reassuming a position of economic consequence.

1. The year to year flow of inheritance as a proportion of GDP is growing from an immediate post war trough, in France at least, of around 5% to almost 20% in 2010.

2. The assumed 5% return on capital is an illusion for the individual. Larger fortunes have access to a greater return than smaller ones. This is demonstrated by ex among college endowments. Harvard and Yale consistently achieve returns in excess of 8% while your local community college might get 3% or 4%.

3. The living standard available to the top 1% of inheritors has surpassed that of the top 1% on the labor income distribution. A top inheritor can expect to earn close to 14 times the average wage of the bottom 50% of workers, whereas the top paid workers themselves only average about eleven times the average.

Bill Gates's grandchildren might not individually see their wealth surpass Gates's, especially with the pledge, but there are many more heirs inheriting chunks that the average upper middle class white collar worker could never come close to earning in a lifetime these days then in the latter half of the 20th century.

This sounds a lot like the old axiom about getting rich. The two best ways to get rich are inherit it or marry it. In other words, nothing has changed since the dawn of civilization.

I'm not dismissing concerns about the accumulation of wealth. For a society to have maximum liberty, you have to make sure the dead don't control the living. A better explanation of current trends may be that great changes in the economic order result in great fortunes being made and then passed on for a number of generations.

If Gates gave his favorite grandchild his money instead of to his Foundation, and they did nothing more than put it into a Vanguard LifeStrategy Growth Fund (80% stock index, 20% bond index), I would be surprised if in three decades time, their wealth hadn't grown more than by 5x in nominal terms (and probably 3x in real) at the very least. Even after taking out a modest percentage annually to live quite well on.

And if a revanchist Soviet Union conquers the United States, they'll take all the money in all the banks and financial institutions, and put the grandchildren of the plutocrats to work at hard labor in the Gulags.

Which is important here, because the probability of Vladimir Putin reestablishing hard-line communism, restoring the Soviet Union, and conquering the United States of America, is much greater than the probability of a hereditary multibillionaire putting the entire family fortune in an index mutual fund and living on a modest percentage of the profits.

Case in point.

The Bronfmans : the rise and fall of the house of Seagram

Author: Nicholas Faith
Publisher: New York : St. Martin's Press, 2006.
Edition/Format: Book : Biography : English : 1st edView all editions and formats
Database: WorldCat
The Bronfman family story is an improbable saga of larger-than-life personalities and bitter rivalries. "Mr. Sam," the man who made drinking whiskey respectable in the United States, built Seagram into the first worldwide liquor empire in the 1950s and 1960s. After Sam's death in 1971, his oldest son Edgar masterminded a major coup when he translated a small investment in oil made by his father into a 25% stake in the mighty DuPont company. But in the 1990s, Edgar allowed his second son, Edgar Jr., to indulge his ambition to become a media tycoon. He reinvested the DuPont stake in Universal, the film and theme-park empire, then bought Polygram Records. But at the same time, he remained in charge of the liquor business, which started to fall apart. Then came the final disaster, when the increasingly divided family sold out to the empire builder of the French conglomerate Vivendi.--From publisher description.

You'll have to excuse me if I don't take seriously the argument that we shouldn't bother over the concentration of wealth because they eventually squander it on bad investments.

If so, what's really the problem with wealth taxation, since the grandchildren will just squander it all some day anyway?

"what’s really the problem with wealth taxation?"

It's effectively a double tax. The money was taxed the first time as income, and it's being taxed again do to some vague need to make the "rich" pay more.

I'd much rather see inheritance taxes, than a wealth tax. IMO, the inheritance is similar to income, and we generally tax income. We don't generally tax wealth, at least at the Federal level.

And in any case, it's the obligation of the side that wants a change to make a decisive case for it. There's no obligation on everyone else to defend the status quo.

That process is something born after the world wars has not seen much of due to the massive destruction of wealth the wars brought about. The capital to income ratio has returned to per war levels. Thus, there is every reason to believe that your probability estimate is entirely worthless, since it was built in a world where relative capital was small.

Something to think about: between 1990 and 2010 Lilliane Bettencourt and Bill Gates both saw their fortunes achieve a rate of return of 13% and shoot up into the tens of billions. During that time, Gates was busy producing the world's most popular operating system. Bettencourt was just watching her father's fortune tick upward, no labor on her part required.

"what’s really the problem with wealth taxation, since the grandchildren will just squander it all some day anyway? "

Why? So the government can squander it? The unintended consequences of government spending are orders of magnitude more negative than anything a socialite might do.

Liliane Bettencourt was when she was still healthy, and her daughter and grandson now are, members of the board of directors of L'Oreal. It is not clear how much labor this involved, but then it's not like Bill Gates is writing much code these days. Regardless, the Schueller/Bettencourt/Meyers family fortune is not invested in an index fund. Like just about every other family fortune, it is being actively managed by the family - whether personally, through a hired team of experts, or some combination of the two. If it grows at 13% per year (and as a L'Oreal stockholder I'm glad it does), then it is because the family's management team is doing a good job. And as a family enterprise only minimally bound by the demands of outside investors, they can plan to do a good job on the timescale of decades with a fair bit of philanthropy on the side.

But they'd have to do an unbelievably good job for Jean-Victor to wind up with a net worth of $300 billion, the tenfold gain that prior_approval postulates as the norm for the grandson of a plutocrat. I'd be the last to complain, seeing as how I'm going to be piggybacking on that growth, but I don't expect it. More typically, it's in the third generation that family fortunes begin their precipitous decline due to personal or professional mismanagement. I'm betting that the Meyers clan will postpone that outcome by maybe a generation.

Now for the interesting question: What happens if someone hypothetically does drop fifty billion dollars into, say, the Vanguard LifeStrategy Growth Fund?

I suggest that r > g is being given way too much attention. Rising inequality in wealth is first derived from inequality in income from wages, the wages saved becoming capital which generates more income; it's the combination of rising inequality in income from wages and the income from wages saved that becomes capital which catapults inequality in wealth to the level that is socially destructive (in Piketty's view). Piketty's mistake, in my view, is that he all but ignores the financial and economic instability that correlates very strongly with excessive inequality: as r falls, owners of capital devote more of it to speculation in pursuit of higher r, bubbles are created, bubbles burst, the financial system collapses, the value of capital plummets, and excessive inequality is corrected. Piketty assumes that, when the financial system collapses, as it did in 2008, governments and central bankers will intervene, as they did in 2008-09, and prevent the value of capital from plummeting while also preventing another economic depression. The paradox, not addressed by Piketty, is that intervention to avoid another depression also preserves the value of capital and excessive inequality; absent intervention, inequality is self-correcting. Of course, the self-correction can be very painful, as it was in the 1930s when the U.S. government and central bank chose not to intervene following the financial collapse in 1929, and the value of capital plummeted along with inequality; inequality in wealth plummeted following the financial collapse in 1929 and remained low for decades. Piketty all but ignores the self-correction because he is European (French): in Europe, the correction to excessive inequality in wealth in the early 20th century resulted from the physical destruction of capital (two major wars), not the destruction in the value of capital as occurred in the U.S. following the financial collapse in 1929. Will governments and central bankers continue to intervene during future periods of financial crisis brought on by excessive inequality? Piketty assumes they will; I don't.

Piketty repeatedly mentions that the violence of the depression and world wars as being the only thing that brought an end to the massive concentration of wealth leading up to 1914. He also repeatedly mentions that there are some potential levels of inequality that he presumes to be politically unacceptable, on the order of causing some sort of tumultuous change. It's weird you say he ignores these things. I think a more sensible reading is that he'd just much rather focus on the more peaceful regulation of the concentration of wealth through taxation than rely on some iffy notion of violent "natural" correction.

We can expect that bill gates grand children will have more wealth than he has if he leaves it all to them. but it may not be a larger faction of GDP. When sam walton died in 1992 his net worth was 65 billion which adjusted for inflation is about $100 billion. The net worth of the walton family is now 150 billion and real gdp has increased by about the same percent. However the market cap of walmart has increased by a factor of more than 5 so it looks like it would have been possible for them to increase their wealth as fraction of GDP just by holding the sock and living off of dividends. If there is a flaw in pittity´s theory it can probably be found in the reason they did not.

Why are you comparing what one individual has/had to what a group of individuals will have/has?

Piketty worst argument is there are no given reasons why all the income has not gone to capitalist. Kevin Drum's simple thesis is that War is the primary reason for this historical reality:

1) War solves both the Keynsian economic problem (Gov spending is high) and the Hayekian problem (War is highest form of Creative Destruction and the winners tended to be the side that best utilized technology since The US Civil War.) Look at the world until W1 & W2 finalized?

2) Why did Post-War period have falling income inequaity? We were in a symbolic (Cold) War that limited capital movements and there were plenty of civil wars still occurring.

3) War destroys enormous amounts of capital and sets back a lot wealth.

In the future, I wonder if the falling global birth rates will control for the falling wages against capital. At some point there could be labor shortages.

Technology, including strategy, has always been the deciding factor. The English defeated a bigger and more heavily armed French army at Agincourt because the English long bow (technology) and Henry was a brilliant leader (strategy). Scipio defeated Hannibal at Zama using better technology (cavalry) and better strategy, allowing Hannibal's war elephants to charge through designated openings in his lines.

Given that, you can remove war from your analysis and replace it with technology. "Technology solves both the Keynsian economic problem (Gov spending is high) and the Hayekian problem."

"Piketty worst argument is there are no given reasons why all the income has not gone to capitalist. Kevin Drum’s simple thesis is that War is the primary reason for this historical reality:"

Except Piketty makes this exact argument. You don't know what you're talking about. Don't pretend.

"Some of the reviews seem to imply that Piketty argues that real rate of return on capital represents the rate at which the wealth of the upper classes grow. Is that right?"

I didn't get that from the first 120 pages, but even so, he wouldn't implied the trend would continue forever.

Structures aren't financed by 3 year real interest rate bonds, which are trading close to -1%. They are financed by long-term bonds. If anything, the benchmark is the 1% rate on the 10 year TIPs. Of course what really matters is if corporations can issue such bonds, but they can't. You could take the nominal rate that a corporation could issue at and then subtract out the differential between Treasuries and TIPs at that maturity to get an idea of the corporations real interest rate.

Here's the interesting point:

"Since structures are already 175% of GDP, this would imply an additional increase of 350% of GDP, more than doubling the overall private capital stock and nearly doubling national net worth. The transition to this level would require such an extraordinary, prolonged investment boom that we would not face slack demand for many, many years."

Well, yes. But we DIDN'T see slack demand for many, many years. And between 1980 and 2008, we successfully masked the transition by progressively reducing nominal interest rates to zero in order to stimulate demand. By 2008, we had accumulated enough debt that even zero interest rates were insufficient to prop up aggregate demand.

Thus, I don't see how the back of the envelope calculation lends weight to an argument against secular stagnation. I see the exact opposite: a very good description of the last thirty years of economic history.

My underlying view here is that we should be thinking about long-run equilibrium in capital markets - if the stagnation is truly supposed to be secular, then we need to tell a quantitative story about stocks rather than just flows.

To get an intuitive handle, let's think about a supply-demand diagram for the steady state, with the capital-output ratio K/Y as the quantity and the real interest rate as the price. (Most simple models actually do imply that steady-state equilibrium is characterized by such a diagram, although you have to be careful.) The shape of the demand curve depends on the long-run elasticity of capital demand, while the shape of the supply curve is more complicated and depends on exactly how we set up the consumption/savings side of the model. (With a single infinite-horizon dynasty, the supply curve is perfectly horizontal, since long-run savings are infinitely elastic with respect to the real interest rate. But you can get more reasonable predictions and a much lower elasticity with a more complex model, like a heterogenous agent model with borrowing constraints.)

Now let's suppose that we have some shock to the supply or demand curve, and we want to think about how this impacts the general equilibrium real interest rate. This effect, of course, is inversely related to the sum of the supply and demand elasticities. My basic point is that under most conventional parameterizations, the demand elasticity alone is large enough that you'd need implausibly large shocks to the supply or demand curves (reflecting implausibly large fundamental changes in the economy) to get a large decline in the real interest rate. This point is very general, and doesn't really depend on the source of the shock.

If the proposed shock is only to the supply curve, then this focus on the demand side is even better, since the (unchanging) demand curve gives us the locus of possible (K/Y,r) pairs. In that case, we can be pretty certain that either (1) secular stagnation is impossible or (2) the elasticity of capital demand is far, far lower than anything conventionally assumed. (I am sympathetic to the possibility of (2), but I want to emphasize that it is the diametric opposite of Piketty, who argues for an extremely high capital demand elasticity.) Moreover, this "shock to the supply curve" actually encompasses most of the proposed mechanisms for secular stagnation, such as a secular shift in consumption/savings behavior or an influx of savings from abroad. In most models, it even includes the case of a downward shift in long-run growth. (This is subtle, since growth affects the quantity of net investment conditional on K/Y, but it does not affect the steady-state ratio of K/Y itself, except via the general equilibrium channel of the real interest rate. One big problem in these discussions is confusion between capital stock demand and investment flow demand.) If you want these mechanisms to drive secular stagnation, you must be proposing either a very unconventional capital demand specification or an absolutely enormous change in fundamentals.

If the proposed shock is to the demand curve, then we have the identification issues Tyler mentions ("reasoning from a price change"), but unless the proposed change in capital demand implies a very low elasticity, the analysis above is still relevant: capital demand might decline, but given any quantity shift in capital demand, you'd only need a small decline in the real interest rate to restore steady state equilibrium. I don't think anyone has proposed a story for why technology or preferences have shifted such that we'll want radically less capital than before. To the extent that they have, usually the stories involve some confusion about the relevant magnitudes. (e.g. you hear about how we're replacing the large factories of yore with lean startups. But manufacturing has never accounted for a large share of the capital stock, and it's been <10% of private fixed assets for over a decade. It's just a sliver compared to residential structures.)

The one downward shock to capital demand that could possibly put us in negative equilibrium 'r' territory would be a collapse in financial intermediation and a large increase in spreads. Anyone discussing secular stagnation should probably concentrate on this case. Still, I'm skeptical, because the vast majority of private fixed capital is in the form of structures (plus land if you're including non-reproducible capital), and for many structures, intermediation is relatively easy - they're fixed in place, relatively easy to seize upon default, often can be adapted to alternative users, etc. Residences alone account for almost half of private structures - what kind of catastrophe would have to happen for mortgage spreads to permanently balloon by, say, 3%? And the need for intermediation can be circumvented with internal funds, which becomes a much more attractive option when spreads explode - the spread-inclusive cost of capital is not the relevant one for all purposes. So while I can appreciate the possibility that a long-term increase in spreads would push down the equilibrium real interest rate, it's still difficult to imagine the quantitative story here.


1. Are you maintaining the assumption that we were far from secular stagnation before? What if we were almost there already, so the required decline in r* is less than you think?

2. Would you agree that secular stagnation, at least in the sense of a very very long stagnation due to r>r*, will happen if the central bank targets a sufficiently high rate of deflation?

(1) Prior to the crisis long-term nominal rates were mostly around 4% or higher, whereas I'd expect long-term nominal rates in a secular stagnation regime to be around 1%. (Reflecting continued short rates around 0%, but the ever-present possibility of a rebound, with movements in the other direction cut off by the ZLB.) So in this sense I don't think we were very close to secular stagnation - there was still a big decrease in long-term yields that needed to happen, and unless the world has a very low elasticity of capital demand, this decrease (assuming near-constant inflation) would imply a very large increase in steady state K/Y.

(2) Sure, at a sufficiently high rate of deflation there will always be secular stagnation. Even a few percent a year in the US context, if other events cooperated, could be enough to do it. My back-of-the-envelope calculations assume that inflation will not decline, or at least not decline by very much. I agree that if the monetary authority was delinquent enough to allow a deflation, it could face some serious problems.

But deflation takes time to embed itself, and we're still far enough away from deflation that I don't think this is a problem - plus the Fed appears willing to take rather drastic measures in case deflation threatens itself. If, say, we don't see outright deflation but instead have a decline in inflation from 2% to 0.5%, that's still high enough that continued zero nominal rates will eventually provoke an investment boom, allowing the Fed to push inflation back up. It would take a very serious shock to push it into a deflation fast enough to induce secular stagnation and become self-fulfilling even at the ZLB.

I don't think it's appropriate to use the actual, realized, nominal long-term interest rates for the pre-crisis period. For one thing, the past 30 years have been characterized by repeated unanticipated declines in the inflation rate. To me, this implies that: (1) actual ex ante real interest rates were above equilibrium; (2) acutal ex post real interest rates were above ex ante real interest rates. Taken together, these points suggest that observed nominal interest rates during that period were considerably above the value that would represent equilibrium based on realized inflation rates. Moreover, there was apparently weird, unsustainable stuff going on in the period before the crisis, and it would appear that such stuff was distorting the relationship between risk-free interest rates and investment. (In particular, the spread between Treasuries and shadow mortgage rates -- by which I mean mortgage rates adjusted for limits to the ability to obtain mortgage financing -- was apparently artificially low, so that, among other things, a given Treasury yield could support more residential investment than would be possible in a sustainable equilibrium.) So I find it quite plausible that if (1) expected inflation rates had been comparable to what they are now, (2) there had been no unsustainable weirdness distorting capital markets, and (3) interest rates had been at equilibrium, that long-term nominal rates would have been well below 4%, perhaps even low enough to be close to secular stagnation levels.

FWIW I don't think financial intermediation collapse is the right explanation. The credit boom of the noughts was surely a symptom and not a cause of the ostensible secular stagnation. And it's hard to argue that the collapse happened before that. We got very close to the ZLB in the early noughts, and presumably only the credit/housing boom (which most regard as irrational in retrospect) prevented us from hitting it. Whatever process was leading to ostensible secular stagnation was already well underway. Perhaps not "financial intermediation collapsed" but "adequate financial intermediation was never possible, and we made a failed attempt." Sec. stag. would suggest that house prices should be extremely high, but our financial infrastructure may never have been able to sustain the appropriate equilibrium.

Andy, as you know I see the naughts differently. Properly measured there was an positive output gap as the Fed lowered i below i*. The productivity surge is the back story. And looking to the absence of inflation as evidence of weakness ignores the possibility that the low inflation was the consequence of strong productivity growth rather than weak aggregate demand.

"I am still waiting for a model of secular stagnation that rationalizes both a negative real interest rate and positive investment, which indeed we are observing in most countries circa 2014."


If interest rates are zero or negative, the hurdle for building new capital should be zero ROIC.

"...especially when you keep in mind that land values would be skyrocketing as well."

Ok, so taking the conservatives most favorite way to "create wealth", "drill baby drill", which I see as pillage and plunder destruction of capital assets because I'm a liberal, let's consider fracking economics.

You have a hundred acres of land as a farmer, and a "wealth creating fracker offers you a "standard" deal, a 17% royalty on the wholesale price, and over the next decade produces and sells $1,000,000 in natural gas, paying you $17,000 and lets say a $3000 bonus. so that averages a $2000 per year return on your capital, the land. But given the lifetime of a fracked well is 7-10 years, in the 11 year your fracking revenue is $0.

How much more valuable is your hundred acres of farmland in year eleven compared to year zero? Presumably you have farmed the hundred acres continuously for the decades before and during and after the fracking, but how much of the increased land value that conservatives assure us will "skyrocket" is due to fracking and depleting the natural gas on the land to create wealth??

If your neighbor refused to allow his hundred acres of land to be fracked, is your land, which had the same "value" before you created wealth by contracting your land for fracking, worth more than his land, or worthless.

If your land is worthless, haven't you accepted a negative return on capital to create wealth?

"If interest rates are zero or negative, the hurdle for building new capital should be zero ROIC. "

No, that's not even close to correct.

"In business and engineering, the minimum acceptable rate of return, often abbreviated MARR, or hurdle rate is the minimum rate of return on a project a manager or company is willing to accept before starting a project, given its risk and the opportunity cost of forgoing other projects. A synonym seen in many contexts is minimum attractive rate of return. As an example, suppose a manager knows that investing in a conservative project, such as a bond investment or another project with no risk, yields a known rate of return. When analyzing a new project, the manager may use the conservative project's rate of return as the MARR. The manager will only implement the new project if its anticipated return exceeds the MARR by at least the risk premium of the new project."

Your first point was correct. TANSTAAFL

You then proceeded to follow it up with an assumption that Capital is a "free lunch" at 0 interest rates. It's not ever a free lunch. No rational investor is ever going to invest their Capital at 0% return for a project with any risk. They'll just keep their gold coins and precious jewels in a massive vault and go swimming in it from time to time.

Now certainly you might find an investor who's personal return is measured in non-monetary amounts who is willing to invest in a project that is personally rewarding. Conservatives tend to refer to that as charity.

As long as bill Gates descendents do not touch the capital-- and only live on the income-- there is no need for them to be ten times as wealthy .

Not touching the capital is something that is ingrained in the wealthy -- at least in the UK.

The problem with this analysis is that it ignores expectations about the future, Keynes' "animal spirits." To say this more neoclassically, the use cost analysis neglects the fact that expectations of asset price growth enter into the user cost equation.

For example, if depreciation is 2.5%, the real interest rate is 2%, and expected house price growth is 3%, so the user cost is 1.5% (think of this as 2005). Now, in 2013, depreciation is the same, the interest rate is -1%, and expected house price growth is -1%, so the user cost is 2.5%. Instead of low interest rates causing a housing boom, pessimistic expectations cause a bust.

So, I think it's easy to understand why very low interest rates might not cause an investment boom: people don't want to invest when they're pessimistic about the future.

Sure. If there is an expected price change, that enters in, and this can be a very big deal in the short run. But I'm thinking about reproducible capital (structures, rather than the land they sit on) in the long run, and a nonzero average price change for reproducible capital in the long run is only possible if there is some secular trend in our relative productivity in making this capital vs. other goods.

Such a secular trend does indeed exist, but it is not large enough to make too much of a difference in the analysis. The price deflator for residential investment, for instance, has declined relative to the overall GDP deflator at an average annual rate of about 0.5% since 1947. If this trend continues, then in principle it means that the user cost of residential structures is 0.5% lower than otherwise - which would make the result of my calculation above even more dramatic. (Of course, there are a lot of other fixes that could be made to this calculation to make it shrink too - I'm not arguing that it only goes in one direction. The more important point is that however you slice it, the numbers are huge and perhaps implausible.)

Matt writes" "a nonzero average price change for reproducible capital in the long run is only possible if there is some secular trend in our relative productivity in making this capital vs. other goods."

If it were true that in the long run the price of reproducible capital like housing tends towards construction costs, which seems to be Matt's claim, then houses in Detroit would be a great investment. After all, houses in Detroit often sell for $10,000, well below construction costs. A boom in Detroit house prices must be right around the corner!

The problem with Matt's claim is that reproducible capital such as housing is long-lived. It's true that a long-run positive price trend can't be sustained, since additional house building will just drive the price back down to construction cost. However, no such mechanism prevents a long-run negative price trend. Falling prices can persist until depreciation depletes the housing stock, which can take a very long time.

So, again, pessimistic expectations about future housing prices (or reproducible capital more generally) can be perfectly rational, and can easily rationalize a negative long run interest rate.

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