The desired stock of savings

Isn't a concept we talk about much in macro. Which is a bit weird, when you think about it. And it's always good to examine the way we think about things, and teach those things.

We talk about households' desired flow of saving, and firms' desired flow of investment, and we talk about the actual flow of saving and investment. We also say that firms have a desired stock of capital, and spend some time explaining how to get a desired flow of investment from that desired stock of capital. Why don't we talk about households' desired stock of savings, and compare it to firms' desired stock of capital, and compare both to the actual stocks of capital and other assets?

I don't know the answer to that question.

We don't always talk about flows. For example, old keynesians like Tobin, and old monetarists like Brunner and Meltzer, would sometimes talk about stocks. But we usually do. (And of course stocks and flows must be consistent.)

Maybe it's the legacy of ISLM.

Maybe it's because of the infinitely-lived agent assumption, typically used in New Keynesian models. Take a stationary economy for simplicity. If the real rate of interest equals the agent's rate of time preference, the agent's desired stock of savings is equal to his actual stock of savings, regardless of what the level of that stock actually is. The desired stock of savings is undefined. (And if the rate of interest is greater/less than the rate of time preference, the agent wants a rising/falling stock of savings, again regardless of how big or small that stock actually is.)

If instead we assumed agents with finite lives, who want to make sure they have a large enough stock of savings for retirement, we could talk about the desired stock of savings, and talk about what it depends on. And if the actual stock of savings were less/greater than the desired stock of savings, we could talk about how agents would desire a positive/negative flow of saving to adjust their actual stock to equal the desired stock over time. And the desired stock of savings would include not just capital, but also land, and government bonds and money. And we could talk about how asset prices adjust to equalise households' and firms' desired stocks of savings and capital with the actual stocks of assets.

And if we did that, we could then talk about how increases in lifespans while retired, and the percentage of people who will be retired, would increase the desired stock of savings, and how that would increase land prices, bond prices, share prices, and the price of money (the reciprocal of the price level). Maybe like this. And all of those things seem to me to be empirically important for the recent past and the near future.

And maybe we would find that the National Income Accounting definition of the flow of "saving", which excludes rising (real) asset prices, is not the most useful definition.

But we can't talk about those things properly, unless we talk about the desired stock of savings.

[I just checked my Carleton online retirement planner, to see if my stock of savings is big enough. It nearly is.]

Comments

[Luis Enrique]

I think Chris "buffer stock of saving" Carroll might have something to say about this - presumably in his models, if an agent's situation changes, their desired stock of saving does too.

[here are his papers: http://www.econ2.jhu.edu/people/ccarroll/downloads/downloads.html]

And this is part of the "balance sheet recession" idea, right? We experience a recession whilst people adjust their stock of saving? (or debt, as case may be)

[Luis Enrique]

there are lots of models of saving for retirement around - mostly OLG? - so do you have in mind better integration of those ideas with business cycle macro?

[Nick Rowe]

Luis: yes, something like that. And maybe, simply, paying more attention to that perspective, in our thoughts and textbooks. And making sure land is in there.

[Nick Edmonds]

SFC models are increasingly used in post-Keynesian circles and these generally involve a desired stock of savings. I think one needs to be careful about assuming that any desired stock-flow ratio is stable over time, and that applies to savings to income ratios, just as it does to money velocity measures. However, most mainstream models pay far too little regard to the levels of financial stocks, in some cases completely ignoring them or sticking them in as awkward add-ons.

[Nick Rowe]

Nick E: we are on the same page. Old monetarists, like old keynesians, thought more about stocks, and about what happened when actual and desired stocks were different. The hot potato process is one of the last vestiges of that, but it only applies to stocks of money. And the desired stock/flow ratios, of which 1/V is one, may fluctuate over time, and cause macro instability.

Take an extremely simply macro model, where land is the only asset. The price of land adjusts until the desired stock of land equals the actual stock of land. And that determines the yield on holding land, which is the only rate of interest in this model. Now add money. Now add capital goods. Now add government bonds.

[Herbert]

Excellent post, Nick. Savings must be derived from desired stocks. Two new papers argue that neglecting this important point is Piketty's main fault:

http://www.iepecdg.com.br/uploads/artigos/piketty1.pdf

https://ideas.repec.org/p/han/dpaper/dp-530.html

[Kevin Donoghue]

Nick,
I'm afraid you've lost me here. This paragraph looks wrong:

Maybe it's because of the infinitely-lived agent assumption....

The representative agent's actual stock of savings must be willingly held, given that the bond market is in equilibrium (which it must be at all times, whether we're in a steady state or not). The desired stock of savings isn't undefined, any more than desired consumption is. Both are derived from the model's parameters.

Herbert: "Savings must be derived from desired stocks."

Like Nick, you've lost me. Again, the orthodox procedure is to derive everything from taste & technology parameters. That's often a tedious and unenlightening exercise, as Piketty is only too willing to point out, but he can hardly be blamed for using the almost-tautological (his description) concept of time-preference.

[Kevin Donoghue]

Messed up my tags there, I hope I haven't created a problem.

[Nick Rowe]

Thanks Herbert! I was going to mention Piketty, then I thought I had better not, because I seem to be the only economist who hasn't read him.

A short history of the last couple of decades: demographics caused households' desired stock of savings to slowly rise, and firms' desired stock of capital to slowly fall, and so asset prices were increasing, and asset yields decreasing. The US then had a negative house price shock, because some owners had too little equity, which caused a desired switch to other assets. Fear of recession increased households' desired stock of savings still further, and reduced firms' desired stock of capital. Central banks said that monetary policy was already loose, because look how low yields are!

[Donald A. Coffin]

Interestingly, Kenneth Boulding's textbook (Economic Analysis, first published in 1941) took a stock-flow approach both in macro and in micro (where it emphasized that production at the level of an individual firm was driven both by sales and by a desire to hold an appropriate level of inventory). (I had to use a later edition of that book once (1973-74)--having been hired at the last minute to teach, with the textbook already selected--and it was extraordinarily difficult to wrap my mind around that approach...It got somewhat easier, though.)

[Nick Rowe]

Kevin: (I fixed the blockquote)

Let me try it this way. Take an individual agent (it doesn't have to be the representative agent), who has a zero flow of desired saving. Hold the interest rate fixed, and give that individual an extra stock of savings (as a freebie). He still has a zero flow of desired saving. His desired stock of saving is whatever his actual stock is right now, even at the same interest rate.

Donald: That is interesting. I would find it difficult to teach too!

[Kevin Donoghue]

Nick, thanks for fixing that. In the NK model I know (Gali's textbook version), assuming log utility which is the simplest case: if r is constant, consumption is a constant proportion of the PV of lifetime income (lifetime being infinite). So if you give the guy an extra bond, he's going to spend a small fraction of it. If his saving was zero before it's now negative. Of course I assume that this lucky individual is the only one getting the freebie; if (somehow) everyone gets a windfall, that's different.

The marginal propensity to consume is very small in that model, but it isn't zero. So how can the freebie go unspent?

[Too Much Fed]

"If instead we assumed agents with finite lives, who want to make sure they have a large enough stock of savings for retirement, we could talk about the desired stock of savings, and talk about what it depends on. And if the actual stock of savings were less/greater than the desired stock of savings, we could talk about how agents would desire a positive/negative flow of saving to adjust their actual stock to equal the desired stock over time."

Explain Warren Buffett, who has more than enough "savings" for retirement.

[Nick Rowe]

Kevin: assuming r=rho, he's going to spend the permanent income from the bond, but no more. So his stock of savings stays permanently higher. It does not return to his original stock of savings, even asymptotically.

[Ralph Musgrave]

MMTers constantly refer to the desired stock of savings. More specifically they refer to what they call “Private Sector Net Financial Assets” which equals the national debt plus monetary base.

[Nick Rowe]

Ralph: but that's a small subset of the stock of savings.

[Herbert]

@Kevin:

"[T]he orthodox procedure is to derive everything from taste & technology parameters. That's often a tedious and unenlightening exercise, as Piketty is only too willing to point out, but he can hardly be blamed for using the almost-tautological (his description) concept of time-preference."

Piketty does not derive savings from desired stocks. He assumes savings to be a constant fraction of gross income which is the old Keynesian style. Because the capital coefficient equals s/g in a steady state, it rises without bound in a slowly growing economy (and becomes negative in a shrinking economy!).

Deriving savings from desired stocks implies that the savings flow vanishes in an economy without growth. Such an assumption makes more sense than Piketty's.

[Kevin Donoghue]

Nick,
OK, we seem to be in agreement about what the NK model says, which is a relief. So I guess the way to meet your concerns is to throw out the usual utility function in which only consumption matters and go for something like U = f(C,A) where A is a stock of assets. Or maybe go for a monetary OLG model.

Herbert: "Because the capital coefficient equals s/g in a steady state, it rises without bound in a slowly growing economy."

I'm not sure what you mean by the capital coefficient here; Piketty's "Beta" converges to s/g. But Beta is just the aggregate value of wealth expressed in years of income. Low (but positive) g is not enough to cause it to rise without bound. You need some other assumption(s) to get that result. For example natural-resource scarcity can do it, as Piketty acknowledges:

...the law β = s / g is valid only if one focuses on those forms of capital that human beings can accumulate. If a significant fraction of national capital consists of pure natural resources (i.e., natural resources whose value is independent of any human improvement and any past investment), then β can be quite high without any contribution from savings. I will say more later about the practical importance of nonaccumulable capital.

Since Nick has made it clear that he isn't much interested in Piketty I'll leave it at that. If I understand him correctly, Nick is taking issue with the whole tradition of treating demand for assets as merely demand for future consumption. Piketty certainly won't quarrel with him on that score.

[Nick Rowe]

Kevin: yep. I think we are in agreement.

I was trying to read one of Chris Carroll's papers (see Luis Enrique's link above). The math was far too hard for me. But I think he's saying that if we take a standard utility function U(C), add a non-negativity constraint on the stock of assets, and add uncertainty, we get something like that desired stock of savings. Which sounds reasonable and plausible to me. But the OLG route might be simpler, and equally reasonable.

[Nick Rowe]

Kevin: "If I understand him correctly, Nick is taking issue with the whole tradition of treating demand for assets as merely demand for future consumption."

I'm not saying something as strong as that. Just that the marginal propensity to consume out of wealth exceeds the rate of interest. Which is what you get with a finite lifetime, or maybe with uncertainty and non-negativity.

[Herbert]

@Kevin

"I'm not sure what you mean by the capital coefficient here; Piketty's Beta converges to s/g. But Beta is just the aggregate value of wealth expressed in years of income. Low (but positive) g is not enough to cause it to rise without bound. You need some other assumption(s) to get that result."

i) Yes, Beta is the capital coefficient (or capital-output ratio) in the usual sense.

ii) Piketty sees s as exogenous and Beta = s/g. If g converges to zero then Beta becomes infinite. If g gets negative, Beta gets negative also. That's nonsensical, in my view.

[Mike Freimuth]

Allow me to just mention that I have such a model. :)

http://realfreeradical.com/2014/07/16/a-model-of-endogenous-money/

[Nick Rowe]

Mike: putting next period's wealth in the utility function is a good shortcut, and works fine for some purposes. But there are some questions it doesn't let you ask. And the one I want to ask is: if people live longer, how does this affect their desired stock of wealth, their retirement age, and the equilibrium rate of interest? Because my hunch is that longer lives, plus greater income and higher demand for leisure (bunched at the end of our lives), is what is causing lower real interest rates.

I'm now thinking of a quick and dirty OLG model to let me explore this without too much math. 2 period OLG, but a fraction of people die at the end of the first period, and the remainder may choose to work part-time during the second period. The young work full-time, and pool their savings in a pension plan that only pays the survivors. A fall in the death rate (longer lives) will cause more saving when young and more part time work when old (postponed retirement).

[Mike Freimuth]

So, that's basically right. Whatever effect living longer has on those things will manifest itself in the shape of their utility function over consumption and next period wealth. So in the context of my model, you would just have to say "assume that living longer changes the utility function in such a way." However, I think you will essentially be doing that in any model, you just might be able to disguise that assumption about the effect of living longer on preferences a little by adding some more bells and whistles. For instance, you could just say what you said:

"A fall in the death rate (longer lives) will cause more saving when young and more part time work when old"

And change the utility function in my model accordingly so that people save more. Everything else is just explanation for why you believe that.

However, digging into that a little, you may find that the aggregate saving doesn't behave the way you expect in that model since the more likely people are to die in the first period, the fewer old people there will be relative to young people which would mean that there would be relatively more savers and fewer dissevers, so even if the savers are saving more, the aggregate saving rate might go either way. (And yes, I realize that this is a reason to build the model, so don't let me stop you haha. But once you figure out whether they save more or less, you can plug that micro result into my model to figure out the macro implications of people wanting to save more.)

[Nick Rowe]

Mike: yep. Microfoundations is a little bit of a fake, in that we can rig them to get the macro results we want. But they do help firm up our intuition. I want to firm up my intuition about the effect of longevity and income on saving when retirement is endogenous.

I'm currently playing with a slightly different setup:

Assume U = log(C)-L, where 0 <= L <= 1 is labour. People consumption smooth, but do not smooth leisure. They work full-time until their wealth reaches the desired level, then they retire.

[Mike Freimuth]

But when they are working they choose the level of L each period (as opposed to working a standard 40 hour work week or something like that)? Or are you thinking "full time" is fixed exogenously and they are just choosing a constant level of C and a retirement age (so consume more and work longer or consume less and retire sooner)?

[Nick Rowe]

Mike: The latter. They vary their point on the consumption/leisure trade-off by varying the retirement date only. If they want more leisure, they continue to work a 40 hour week, but retire earlier.

Clearly that's a simplification, because there are two margins. But notice how people smooth consumption of goods much more than they smooth consumption of leisure. Around age 65, their consumption of leisure suddenly jumps up, and it's a foreseen jump. There must be a non-convexity somewhere, either in technology, or in preferences. We choose to consume leisure in lumps, with small lumps on weekends, bigger lumps on annual holidays, and a massive big lump at the end of our lives. Over the centuries, as we have gotten richer, we have chosen to consume more leisure. But nearly all of that increased leisure has been consumed at the end of our lives. People didn't use to retire; they worked until they dropped.

But we don't look at it that way. Instead we think: "People retire at 65, just like in the olden days, and it's just that we happen to live longer past 65, unlike in the olden days."

[Jacques René Giguère]

Nick: 65 is an historical accident. Political negotiations in Germany in the late 19th century.

[Nick Rowe]

Jacques Rene: yep. Bismark in Prussia, wasn't it? Because almost nobody lived past 65 back then, so it was cheap to pay pensions to anyone who did. But 65 seems to becoming much less of a fixed point. Some retire younger, and some older.

[Jacques René Giguère]

Essentially Bismarck asked: "How many years of pensions for renouncing revolution?" Working class Germans thanked them by their loyalty to II and III Reich. Marx was wrong on that. Proles do not unite if you pay them to be divided...

[Mike Freimuth]

I feel like the non-convexity is more in the constraints than in the preferences. For instance, you start getting social security at 65 (at least in the U.S.). If your work is physically demanding, you get less effective and maybe you get more tired or something (though that is in the preferences) but for some reason employers and workers resist gradual decreases in wages and hours which would be commensurate with these changes and so they just cut it off at some arbitrary point. It's probably largely a transaction cost story: it's easier to just retire everyone at 65 than to constantly monitor their productivity and adjust their hours and wages, though 65 does seem too young nowadays, especially with most jobs not being very physically demanding. I bet you would find that people who are self-employed or otherwise have the ability to adjust their hours on the margin at will, would smooth labor more.

Similarly, there's a non-convexity in the constraints with regard to weekends and vacations. You might prefer to spread a trip to Hawaii out over the whole year, taking a few minutes every day, but that's not really an option. The weekend, like retirement and pensions and the like, is also basically a political construct, not necessarily an organic manifestation of individual maximization in the context of free labor markets.