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Two great points, and perhaps aspects of the same phenomenon: in order for interest rates to be zero, EVERY decision margin needs something weird going on. We get zero or negative rates in some models by proclaiming "no decisions on this margin!" (land use or labor timing). Formally, this is done by not mentioning the decision, and looks just like other simplifications. But it is not innocuous.

Or maybe people are uncertain that they will be ABLE to work in the future and want to hedge against disability.

There's also a characteristic of culture called Uncertainty Avoidance (see Hofstede), which is high for many cultures and for many people, meaning that such people like to avoid uncertain or ambiguous situations and tend to save for unexpected circumstance.

reason and glen: that is probably part of the reason for some saving. But insurance would, in principle, be a better solution for uncertainty, moral hazard aside.


I think you need to make the distinction between real interest rate and real return on investment. A saver can swap between bonds and equity, depending on which asset class offers the higher prospective real rate of return. A saver would only rejoin the prospective work force if neither asset class offered a positive real rate of return OR if the rate of return on an asset class was conditional on that person maintaining employment.

For instance - stock options with very long holding periods. Any options left after a person retires / leaves the company become worthless.

In the past it made sense to retire younger because life expectancies were lower and more jobs involved manual labor. In 1950 a 60 year old probably wouldn't have had much work left in him. I think it just shows how powerful habits and traditions are that we still do this today even though it is not in our best interests.

Nick: "Which will diminish more quickly as I age: my ability to give an economics lecture; or my ability to paddle my canoe? It's not obvious."

If your ability to paddle a canoe decreases - so what? As long as you can get the canoe to go more or less where you want it to go, who cares? If it takes a little longer to paddle up to the Billings rapids - well, that just leaves more time to check out that heron nest on the south bank of the river, just downstream from the bridge.

But if you are no longer able to give a coherent economics lecture, then students suffer. This would not be an issue if pay was linked to productivity, or if there was some system for identifying and working with incompetent faculty members.

I'm hesitant to post this because (a) I didn't actually read your post and (b) you might decide to retire, and then where would we be?

But I suspect that, in a world where pay=marginal value product, your argument is right.

Frank: there are many assets, with many rates of return, but models of secular stagnation and over-saving say all will decline.

Rene: The biggest difference is probably manual vs non-manual labour. But yes, it may take time for customs to change.

Frances: an hour or two on the Rideau river maybe, but a few days in La Verendrye may be more of a stretch. Portages especially.

I work as an investment banker and intend to never "retire", only work "less" with increasing age. My father was a manual labourer all his life, as was his father before him, and "retirement" was the planned inability to continue working at the work he did all of his life. He could conceivably have gone on to do some different work, but saving for retirement made more sense to him.
There are still (and will likely always be) many people who do work that is physically/mentally consuming, for which there is a logical age cut-off (firefighter, pipefitter, welder, crane operator, airline pilot, etc.). For these people, planning for retirement makes sense if they view their vocation as their life's work, and they expect no satisfaction from an alternative line of work (assuming that their retirement hobbies would be preferable to work that they were in a position to do after the age of retirement).
The real question, I think, is whether there should be an assumed general "retirement age" that applies to everybody across the economy, rather than the assumption of a variety of arrangements.

I'm not sure what the most recent behavioral research has to say about this, but I know that there is evidence that people sometimes prefer increasing consumption paths over decreasing ones (I'm taking this from Federick, Loewenstein and O'Donoghue (2002)). Of course a preference for increasing consumption paths runs completely contrary to present-biased behavior. Which is just to say that time preference is probably more complicated than our simple discount-and-smooth models. Sometimes people like to save the best for last.

FWIW, labor force participation in the US has been increasing for workers age 55 and over since the mid-1990s, This is true of all age groups for whom participation rates are reported (including age 75+), for men and women, and across ethnic groups. So perhaps norms are changing.

In addition, the shift from defined-benefit to defined-contribution retirement plans may have reduced the cost of continuing to work.

Finally, I will say (speaking personally) that even continuing an academic career full time can become problematic as one ages. It's fairly common for people's energy levels to change, and for circadian rhythms to change, in ways that don't always fit well with standard work-day definitions. (On the other hand, I continue to teach part-time...a decision that is clearly not driven by the financial rewards of the activity.)

Age discrimination counts for a lot. I think most would prefer to prefer to even this out, or even hope it would, but only those willing to signal their dedication by overworking when young are likely to be kept on while old while those that try to even this out will be relegated only to lesser and lesser work, lower paid and less stable with increasing longer bouts of unemployment, until the effort of work exceeds the rewards from it or it and the time and effort spent on finding it. In part this is due to higher incomes and spending, turning into lower incomes and spending, and increased wealth diminishing the significance of the latter further, while the less affluent redouble their efforts even at diminishing returns to hold on to what work there is, making it less attractive to even the marginally affluent. Ageism enters in multiple ways, experience becomes overpriced, skill becomes outdated, track record becomes the past, ideas become stale, promise becomes old, optimism becomes cynicism, hope, despair. I don't see even a zero real interest rate or static population curing ageism, though lack of ability to retire may keep some working. We could even see a return to multi generational living. With a stable population, no need to add housing or buy it but inherit it with services provided to the elderly.

Off topic.
Nick, does your distinction between temporary vs permanent changes to the monetary base depend on Ricardian equivalence? Or is it strictly a quantity of money distinction that shows up in pq=MV.

Hope that made some sense.

Is it not just that there is a dramatic change in our ability to work? I don't think it is a gradual decrease from 50 onwards.... So, make hay while the sun shines, then stop ... Probably optimal.

i think there might be a stickiness explanation. wages are sticky downward if you stay employed, but if you have an employment lapse, especially by choice, the floor is at zero again.

"Why don't people work part-time when young, and work part-time when old, and save nothing for retirement, because they don't retire?"

Part answer: Shit happens, and the older you get, the more likely shit is to happen to you.

Part answer: Retirement does not necessarily mean that you stop working. You may work, but for yourself, not other people.


"...but models of secular stagnation and over-saving say all will decline"

Didn't you just complain that models of secular stagnation don't include land? Do models of secular stagnation include equity?

Great post, thank you Nick (as always). I have a couple of thoughts about what you said:

1) What if savings becomes decoupled from any future expenditure plans. For example, say certain people amass wealth in vast quantities far beyond what they, or their children (or even grandchildren) will ever consume. A new class of billionaires! They want to have and bequeath to their descendants the power and influence that only extreme wealth can bring. Or, they simply want the next generations of their family to be able to live off the interest of their wealth far into the future. In any case, their motive is not future consumption (at least not in any foreseeable future). This isn’t to say this is necessarily happening now. But couldn’t this cause a stable equilibrium with a negative real rate irrespective of land or financial innovation?

2) Why do we focus on the real rate being *strictly positive*? What if real GDP per capita is growing at 2% and the natural rate is 1%. Isn’t that a sort of negative rate? I’m not sure about that myself.

Thanks again!

Great post. I would choose a pay cut in return for an increase in leisure but feel I have to either work a lot or not at all in my current line of work. I can't lever down to my optimal number of hours. But I am frugal and look forward to early retirement aka financial independence.


I think your intuition is spot on. It boils down to a substitution effect vs. an income effect from the level of interest rates, though, I think - do I work extra hard to catch up to the income I'm missing because interest rates are lower or do I just forget about it altogether and enjoy more leisure. I tend to think the leisure aspect should dominate here, unless hours worked is very sticky.

A thought that is very close to yours, might the expected path of interest rates be very influential as well? If I think interest rates will fall, I need to work as much as possible now to accumulate capital and lock in that interest rate, and the opposite effect for rising interest rates?

Nick, isn't this most likely an increasing returns story?

Working full time make me more efficient (learning by doing, building human and relationship capital) and so it ends up being better for my discounted lifetime utility to work in lumps.

Why don't I alternate periods of full time work with periods of leisure at a higher frequency? Well, wealthy people sometimes do! For most of us though that would most likely be due to liquidity constraints, I can't borrow enough against the future labour income when I don't yet have a job that gives a guide to how much income that will be.

Adam P: part of it very probably is an increasing returns/liquidity constraints story. But some people do take a "gap year" between school and university, or switch careers with time out in between. Or might want longer holidays or shorter working week coupled with a later retirement. The question is: whether that might become a lot more prevalent as real interest rates fall?

Suppose, for example, the real interest rate drops by 2%. By the rule of 70, that halves the relative price of current leisure vs future leisure over a 35 year working life. We should expect to see some sort of response to such a big relative price change. As Donald Coffin says, maybe we are starting to see some sort of response like that already in the data, with higher participation rates for older people and lower participation rates for prime-age males.(Or maybe it is caused by something else.)

Johnny: I'm not sure about the income effect. For every lender there's a borrower, so what makes one better off makes the other worse off. But I confess I haven't thought much about income effects in an OLG framework.

jonathan: thanks! Yep, I think the increasing returns story, as Adam says, might be why it is hared to have flexible hours. Plus we need to be at work the same time as everyone else is, in some jobs, so we can't change hours for individuals. But if everyone wants to change together, it may happen.

Mark: thanks!

1. Take a stationary economy, for simplicity. Suppose land rents were positive. If real interest rates were negative, what would happen to the equilibrium price of land?

2. Yep. We get dynamic inefficiency (a stable Ponzi scheme can make all generations better off) if the real interest rate is permanently less than the real growth rate. I ignored growth here, to keep the story simple, but it should still translate.

Frank: some models, like Diamand 65, do include capital. You can still get dynamic inefficiency, if the depreciation rate is high enough.

Min: yep. But one of the shit things that can happen is that you can't do some leisure things you wanted to do. "Should I see the world now, or wait till I'm retired? What if I'm unable to travel when I retire?"

babar: true. But some brave souls still take time out. Or are forced to switch careers anyway, so might as well take time out then rather than later.

Robert: yep. But if our capacity to do leisure things deteriorates at the same rate as our capacity to work, it's a wash.

Lord: OK, ageism would tend to motivate taking leisure when old rather than when young. I don't know how big a force it is.

Donald: yep. Though part of older workers' increasing participation rates may be just that they are healthier, living longer, and are younger on average (early boomers are now 65) than they used to be. Declining participation rates of younger males may be evidence as well.

Brad: yep, at least some of us like to store up pleasures for the future, and enjoy anticipating them, even at 0% real interest rates. But even so, relative prices of current vs future pleasures (the real interest rate) should affect our choices.

PelinoC: Yep. Manual vs non-manual work will make a big difference. And manual work is declining. What matters is whether our leisure pursuits are more or less manual than our work. Like a prof who enjoys canoeing!

Miami: I don't think it is affected by whether Ricardian Equivalence is true or false.


"Frank: some models, like Diamond 65, do include capital."


Equity = the residual claim on any asset after all debts associated with that asset are paid off
Capital = the factories, machinery and equipment owned by a business and used in production

Diamond '65 includes factories, machinery, and equipment owned by a business (capital). Diamond '65 includes taxes.

But Diamond '65 does not appear to separate claims on that capital and taxes between debt and equity.

My question was - "Do models of secular stagnation include equity?" not "Do models of secular stagnation include capital?"

Frank: if I own capital, I own equity in that capital. Stop now.


Yes if you own capital, you own equity in that capital - I am not disputing that. However, you can own equity on more than capital assets, and you can own debt obligations on capital goods.

Do models of secular stagnation include equity claims on both capital goods (means of production) and noncapital goods?

Frank: see where I said "Stop now."?


Insurance was the solution. A DB Pension is a life annuity with serialized funding over a working life. A DC Pension can be annuitized but this is not required in Ontario.

Determinant: a DB pension plan isn't strictly an insurance policy. A pure insurance policy would only pay out if you were unable to work.


Absolutely. I am glad that I lived (and worked) in Japan when I was young. :) If you can bum around abroad when you are young, I say go for it. :)

Contributing to the notion of retirement is the expectation of wage growth with seniority. In traditional "career" employment models, a worker's wage increases with time at a rate faster than the wage of a new hire (that is, they climb the corporate ladder or advance in the pay scales or whatnot).

That encourages a clumping of labour, where it is economically advantageous to work for a period and then make a discrete break for leisure. The transition back from leisure to the workforce loses the advantage of seniority.

This is less prevalent in a more flexible economy, where individuals more freely transition between jobs over a working life. If an individual will earn "entry-level" salary a few times over their life, then there's less disadvantage in taking some time off between jobs.

You forgot about the young. I mean really young... Won't somebody please think about the children?


No. You're stumbling over the concept of insurance. Whole Life Insurance and Life Annuities are duals of each other with respect to mortality and payment structure, but they still both insurance. A DB pension is a life annuity with fancy funding arrangement. It's longevity insurance, it's been around for 200 years.

A whole life policy has me (the insured) make a series of payments over my life and then my estate will collect a big cheque at the end. The insurance company takes a risk on how long a life and hope I live a long time so that I make plenty of payments.

A life annuity has me (the annuitant) pay a large single premium in return for a series of payments for the rest of my life, the complete opposite of whole life insurance. The insurance company again takes a risk on how long I live, but hopes I die soon because they will have to pay out less.

In a DB pension, the pension sponsor in effect pays itself the premium and acts as the life insurance company to its pension beneficiaries. Which explains much of what went wrong with DB pensions in the private sector.

A series of payments with a single large payment in the other direction which bears risk with respect to mortality and the life expectancy of the policyholder is by definition insurance, of which whole life and life annuities are two variant species.

Nick, thanks for your reply regarding savings that is not associated with future consumption. I’m so sorry for the long comment ahead but I think I have some valid points to make. If I may:

1) Rents on land can always be lower than the risk adjusted costs of owning land. All land requires some degree of capital and labour in order to generate income. If I own some wilderness, I have to enforce limits on the number of fish people can catch in my lake so it is not depleted. I need rangers to make sure people are not cutting down my trees, starting uncontrolled fires, or dumping garbage. I need to make sure people are not using my land without paying me for it. My land value can go down due to vandalism or natural disasters. If I own urban land my income stream may be volatile yet I am subject to property taxes and legal risks. Even idle land requires one to build and maintain a fence to keep squatters away; someone has to check on it regularly; and it is always subject to potential losses. *Even vacant land that is not subject to property taxes and that is so degraded that no amount of abuse can diminish its value further is subject to risks of law suits or being forced by the government to be sold for a lower real value than was paid*.

2) For investment to have positive real returns in equilibrium, it *has* to be tied to future consumption (doesn’t it?). Isn’t there an implicit assumption in all the models that savings will be spent on consumption eventually? How can you have profitable investment for the sole purpose of generating more savings? If I’m correct, then saving more than what will be consumed in the future can drive the real rate negative (as long as my point 1 above is correct). If wealth provides a degree of wellbeing beyond its consumption value (say, prestige), then there is an incentive for saving more than future consumption.

3) If points 1 and 2 are correct and you perhaps relax some assumptions regarding consumption smoothing, then in the real world you can have periods of “secular stagnation” whenever the financial sector is not able to intermediate between current savings and future consumption (or rather, current investment *for* future consumption). Since current investment is limited to current technology (and assuming a limit to profitable R&D spending), issues around population growth, retirement saving, and technological change can cause such a period of “secular stagnation” because they can reorient the flows of saving and consumption in ways that interrupt the financial intermediation-ability of these flows even if there is not excessive saving.

Thanks again! So sorry for the length. These are just my thoughts. Do please let me know if I’m somehow missing the boat here.

Determinant -
An old joke goes: "Life insurance is a bet you make with the insurance company. They're betting you'll live, you're betting you'll die, and you're hoping they win." With a life annuity, you switch sides of the bet with the company, and you hope you win this time...


My capacity to watch Newcastle United perform dismally on a Saturday afternoon, as I drown my sorrows in beer, is increased with age....


There would not be an equilibrium price. First the price of land would rise sharply, then speculators would jump in and prices would go beyond the levels for which there is a large enough market to maintain the price growth. Then, due to a mix of volatility and psychological factors, there would probably be a large crash in prices and people would say there had been a housing bubble. But then prices would start to rise again... I guess we'll see what happens next.

Ken Schulz:

True, and I've heard it before. But don't get me into unilateral vs. bilateral risk.

yes it occured to me you might answer that insurance is the answer. But in insurance, you insure a particular risk, and get bombed if another risk ends up hitting you. Savings is flexible insurance. Private insurance has all sorts of problems with it (not just adverse selection and moral hazard).

In general it seems economic modellers want to avoid looking uncertainty in the eye. Uncertainty is really important in driving the real world.

I'll post this again, because my previous post got lost. Apologies if it reappears. Basically this a slightly different way of saying what Min said

I actually thought when I posted before that you might suggest insurance as the solution. But I'm a private insurance skeptic. Insurance never seems to pay when you need it (partly because you have to pay now and only receive in the distant future when your counterparty - which has a financial interest in not paying - is an unknown quantity both in financial status and policy, and partly because you insure against something exactly specified, which may be different from the eventuality that you actually face). Saving is a form of non-specific insurance (as is general social insurance such as a citizen's basic income). Given uncertainty increases with time (we are bound to be able to forecast better for the next ten years than for twenty years ahead).

A related question, why can't I get annual pay raises in the form of reduced hours work, so instead of getting paid 10 per cent more I get to work 10 per cent less for the same pay. If I had to choose between a 10% pay increase or 5 extra weeks of vacation (assuming 250 working days a year) I'd probably take the latter.
I imagine the reason my employer doesn't let me do that it's less costly for her majesty (my current employer) to adjust how much she pays me than it is to adjust how much I work. In the first case she just borrows a bit of money, in the second case she has to go find another employee who can do my job and is willing to work five weeks a year and then train him. And I think you could make the case that one guy working full time is better than two guys whose part time hours add up to FT.
I'm not quite smart enough to put all this together in economic terms, but I'm pretty sure the reason most people work steady until they're 65 and stop, is related to why most people work steady from Monday to Friday and then stop, and also work steady from 9-5 and then stop.

Determinant: I get the point that, for a person who retires, a life annuity is longevity insurance. But that assumes a person retires whether or not they are able to work. Drop the assumption of retirement, and what people would need is disability insurance.

Kailer: I think Adam P above may have the answer to that one. If there are some fixed costs to the employer, regardless of how many hours you work, the employer will be worse off if you take a 10% pay cut and a 10% reduction in hours worked, because those fixed costs don't fall by 10%. Plus, if you are part of a team, your working 10% less may reduce the productivity of the other members of the team.

You have to consider that as people reach retirement age the utility of jobs available to them decreases. They will be less enjoyable and poorer paying. When that is not true, people often don't retire.

Why would there be a concept of mandatory retirement age if there weren't a significant number of people who would otherwise continue working?

As for your insurance idea, try comparing the price of such insurance against the actual savings of the bottom 3 quintiles. How much insurance would those savings buy? Retirement is an aspirational goal to those who can never afford to retire.


That's what pensions are. Normal disability insurance is not available for people over age 65. As the probability of disability approaches one, we just drop the disability assessment and give people an annuity.

Given age and the ability to fund a premium through payments, it is easier to just give people life annuities. Insurers won't buy a "pig in a poke" and the risk of disability for those over 65 is just too high.

Retirement always struck me as a polite way of framing the replacement of worn-out machinery. In applications where the work doesn't tend to wear-out or otherwise damage the human machine, we probably see much less 'retirement' (e.g. Profs vs. Miners). Sure, the humans slow down, but not so much that it's worth replacing them.

Also, it's demoralizing to see a decrepit old labourer struggling away. It reminds the other labourers of the dismal fate that awaits them. On the other hand, a spry old country doctor or eccentric economics Prof gives everyone hope that their twilight years might not be so bad.

I don't think it's actually leisure that is the end goal, but freedom. Leisure is perceived to be the only way to experience freedom. If that perception changes, so might change the nature of the utile for which consumption is smoothed.

Mark and reason: apologies. I just found your comments in spam, and rescued them.

re disability insurance, it is a good example of the limitations of insurance here. The problem is that it is not just well defined disability that is the problem. If the skill I have becomes useless in thirty years, maybe my disability is having enough time to recoup the necessary investment in retraining. Maybe my wife becomes seriously incapacitated and needs full time care. Insurance works best with high cost, low probability events. High probability events are much more difficult. And if you have saved for continguencies that don't arrive, you can just use the money for more leisure. It really is impossible for people to reliably plan their lives thirty years in advance.

I'm almost tempted to add to the post above - unless they are tenured professors - but I guess that is just too mean.


Isn't the seeming inconsistency between what we should want and the simplified facts predicted by the OLG model, really a function of the simplification of facts mandated by the OLG model?

Do young people save? I wouldn't suggest that to any of your undergrads, who are probably actively dissaving (either by borrowing to fund their education (or trips to Europe or homes) or sponging off their parents - implicitly borrowing against future inheritances). For the next few years after the graduate, they likely will be savings, though perhaps not at a rate that permits them time for leisure (e.g., you can't amortize your student loan over your expected life). Then they may have a period with little or not savings or leisure (when they have children). They don't start any really savings until their 40/50s, as they reach their peak productive years and kids become less parasitic (are they really "young"?), at which point, you would expect them to devote less time to leisure (given that the opportunity cost of leisure rises with productivity)

To be sure, you might quibble about my characterization of borrowing by the young as dissavings. After all, those debts are incurred to acquire valuable assets (human capital, houses, vague memories of drunken carousing in Europe). One might argue that on the balance sheet of life, that isn't dissaving. Fair, but human capital is only of monetary value if used, and its hard to eat houses and pleasant memories.

More to the point, most people have real barriers to enjoying any extended leisure time when they are young - we call them children. I seem to recall their being recent psychological research that having children makes people less happy, likely reducing the return to leisure (any parent will attest to the fact that at the end of a vacation with their children, they typically can't wait to get back to work). Human biology (and sexual preferences) being what they are, people tend to have children when they are young (in the OLG sense of the word), which tends to impose fairly limited constraints on leisure time when you are young.

Bob: one of the good things about the Eggertsson Mehrata paper is that it did a 3 period OLG model. The young borrow, the middle-aged save to pay off debt and accumulate assets, and the old then consume their savings. But for the retirement question, we can simplify by combining the young and middle-aged. In other words, people are "young" until around 65, then "old" after 65. (Sounds good to me!)

We need to remember to count the saving done by the young through CPP and the employer's pension plan too.

Would I be totally misreading your argument to say that "young" people go to work to escape the kids, and only retire when they can safely do so, and have fun without the kids getting in the way!


No, I think there's a component of that. More seriously though, I think the argument, inelegantly made, is that hitchhiking through Europe with a 2 year old isn't a lot of fun, while doing the same trek by cruise ship 30 years later is. We don't devote time to leisure when we're "young" because we have other, more important things to do.

Or may be do devote time to leisure when we're young. It would be helpful to think about what we mean when we're discussing "leisure" in the OLG model. Think about what happens if we define leisure simply as not engaging in paid work (capable of giving rise to savings) - which I think is how it must be envisioned in the simple OLG model. A good chunk of the population (traditionally, woman, although that's slowly changing) devote a good part of their youth to "leisure" (so defined), namely raising children (whether they're out of the work force entirely, or working part time, or with reduced hours/responsibilities). That's not what anyone of us think of as being "leisure" in any meaningful sense of the word (I love my kids, but leisurely they ain't), but that's "leisure" for the purposes of the OLG model. Moreover, in that model, the working parent (traditionally male, but again that's changing) may be working not to save for the future, but to fund the "leisure" of the non-working parent. Or perhaps, both parents are working so that they can afford to hire the substitute "leisure" of a third person (a daycare, a nanny, the lady down the street).

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