An individual who decides to save for retirement has a choice between a number of different savings vehicles: stocks, bonds, real estate, etc. What are the choices when we aggregate up to the economy as a whole?
I write this post in response to an email from someone who is knowledgeable about the savings vehicle question at the individual level, but was trying to aggregate up to the macro level, knew that aggregation was problematic (the paradox of thrift, for example), had read a couple of my old posts, and asked for my assistance.
The national income accounting identity S=I+G-T+NX (saving equals investment + government deficit plus net exports) may be useful, but should not rule our thoughts. Because the definition of "saving" that it uses may not be the only useful definition.
To be semi-concrete: suppose the government decides to encourage people to save more for their retirement. Where can the extra savings go?
Let's start with S=I+G-T+NX, and see how far we get.
1. NX. Increased net exports (reduced net imports). Lend more to foreigners (borrow less from foreigners). If I save more, by consuming less, or by earning a higher income, I lend a larger part of my income to everyone else, and increase my "net exports" to everyone else. Everyone else is a foreign country, in the individual experiment. A "small" open economy, which has negligible effect on the rest of the world, is just like an individual. We don't ask what the "foreigners" will do with our savings. But this isn't really macro (apologies to open economy macroeconomists). We can't all increase our net exports.
2. I. Increased investment. "Investment", like "saving", has a particular meaning in national income accounting. It means "producing more means of production". We all consume less and invest more, which means we produce fewer consumption goods and more investment goods. Factories and machines are the archetype. But we should include investment in software, research and development, and human capital too. And also consumer durables, like houses and cars. A house is just a machine that produces a flow of output services; we call those services "somewhere to live".
3. G-T. Individuals can save more by consuming less or earning more, and lend more to the government, just like we can lend more to foreigners. And just as we don't ask what foreigners will do with our savings, we don't ask what the government will do with our savings. But this is clearly problematic. Government is not like a foreigner. We own the government (or the government owns us). Lending to the government is like lending to ourselves.
The S=I+G-T+NX identity is useful for some purposes, but is not the most useful for this purpose. The question of saving for retirement begs for an overlapping generations (OLG) perspective, and that perspective is entirely missing from S=I+G-T+NX, because it aggregates across all generations alive in any given year.
Let's start again from the beginning.
Young people are working and earning an income from producing goods. They want to retire (stop working) when they are old, and yet continue to consume goods. How can they make this happen?
Start with a very simple OLG model: land and labour produce wheat, which can be stored. In this model, there are two ways a young individual can save for his retirement: buy land that he can sell for wheat when he is retired; store wheat that he can consume when he is retired.
Though terribly "unrealistic", this very simple model is much more useful than the S=I+G-T+NX accounting identity.
1. Buy Land.
Each individual who wants to save more by buying more land can do so. But they can't all do this. What happens if all individuals decide to double the value of their savings in terms of wheat? The price of land doubles. Does this doubling of the price of land give them a better standard of living when they retire and sell their land to the next generation? Yes, but only if the next generation also doubles its saving too. The value of each cohort's land when it retires depends not on how much it saves, but on how much the next cohort saves.
The land in my simple model works exactly like an unfunded PAYGO pension plan. If the young in cohort B double the value of their savings in land, it is the old in cohort A who benefit, by selling land at twice what they paid for it, and the old in cohort B only eat more wheat if the young in cohort C double the value of their saving in land too. If one future cohort "breaks the chain", and does not double the value of its saving in land, the old in the preceding cohort are worse off than they would have been otherwise; they consume less wheat when young, by paying double the price to buy the land, but consume no more wheat when old than they would have without doubling their saving.
The land in my simple model also works exactly like government debt. If the government cuts taxes (or increases transfer payments) for the current cohort, that cohort is better off. It is exactly as if the government gives bonds to cohort A, as a freebie, and cohort A, when it is old, sells those bonds to the young in cohort B in exchange for wheat. Cohort A eats more wheat. Provided the government rolls over the debt plus interest, so that cohort B pays no more taxes than before, cohort B is no worse off (and may be better off). But if some future government "breaks the chain", by increasing taxes to pay down the debt, or simply pay interest on the debt (and it may be forced to break the chain to prevent the debt/GDP ratio growing without limit so the bonds cannot be rolled over) the cohort that pays the highr taxes is worse off.
The simplest way to think about PAYGO pension plans and government debt is to ask instead what would happen if the government issued bonds and bought land. The rent on the land pays the interest on the bonds. A compulsory PAYGO pension plan is like the government buying land on your behalf.
Don't take "land" too literally. Saving by buying antique furniture, old houses, or old paintings, is also just like saving by buying land.
2. Store wheat.
Buying land does not count as "saving" and "investment" in national income accounting, even though it may push up the value of land, and provide a way for everyone to have a better standard of living in retirement (provided no future cohort "breaks the chain"). Storing wheat does count as saving and investment, because wheat put into store is a newly-produced good that is not being consumed. Storing wheat is a form of investment that has a zero real rate of return. (Or negative, if storeage is costly, or if some stored wheat is lost to rats.)
Investment in machinery is a hybrid between storing wheat and buying land.
When we divert current production away from consumption towards investment, we consume less wheat today, but can consume more wheat in future. But investment in machinery may (or may not) provide a higher rate of return than storing wheat.
When the current cohort buys machines, it can sell its stock of those machines to the next cohort to fund its retirement, just like land. Provided the next cohort does not "break the chain", and wants to save too, otherwise they won't pay anything for the machines.
Demographics will matter. Take the extreme case, where there is no next generation, and the population dies out, because nobody has any kids. Buying land won't work, because there is no next generation to sell it to. And if the machines require labour to operate, that won't work either. The only feasible investment vehicles are: storing wheat; building robots (labour-saving capital goods).
Nick,
Though terribly "unrealistic", this very simple model is much more useful than the S=I+G-T+NX accounting identity.
No.
This OLG model dynamic is entirely consistent with and captured by the relevant accounting identities.
In the OLG land model, the young cohort that buys land is saving. But the old cohort that sells it is dissaving – because they are consuming with the proceeds of the land sale.
And for each discrete time period, saving (young) + dissaving (old) = 0 = investment.
Furthermore, the gain in land value and purchasing power from young to old is then captured in flow of funds accounting (like the value of equity stock over time). That is not a NIPA saving flow, but it is an adjustment in the value of stock savings, as per standard flow of funds accounting.
Flow of funds accounting is a necessary complement to NIPA for a fully coherent set of accounting statements. That is generally understood. Please do not shoot NIPA for being required but not being sufficient when it is generally understood as not sufficient even in the pure accounting context.
It is not NIPA which is inadequate. It is the misunderstanding that NIPA is a necessary but not sufficient component in the full set of required accounting statements.
NIPA + flow of funds fully captures the record of your model here.
Posted by: JKH | March 10, 2014 at 10:27 AM
JKH: fair enough. But suppose the young have just bought all the land off the old, then suddenly decide to double their savings. The price of land doubles, but there is no flow of funds at all (until next period, when they are old, and the flow of funds (i.e. wheat) from young to old doubles).
Posted by: Nick Rowe | March 10, 2014 at 10:38 AM
Flow of funds accounting includes balance sheet revaluation as a standard feature.
As in the Fed flow of funds reports for example.
Maybe better to say that a coherent set of statements includes income (NIPA), flow of funds, and balance sheets - but flow of funds reporting is generally understood to connect balance sheets at different points in time, including revaluation effects such as stock and real estate.
I think the fact that micro saving can be negative but macro saving can't (i.e. the gross saving measure as in GDP) is an important conceptual construct in these sorts of problems.
I guess my point is that I think the income accounting identity and NIPA gets a bad rap as a straw man in the sense that it is accused sometimes of not being sufficient when it is fully understood by accountants as not being sufficient (but necessary) in the same sense - and that there is an accounting complement in flow of funds (including revalued balance sheets).
The entire book 'Monetary Economics' by Godley and Lavoie is a run on this theme - fusion of NIPA and flow of funds accounting.
I think a lot of what you are interested in with such OLG models and non-investment themes for saving for example can be worked in under that larger umbrella.
Posted by: JKH | March 10, 2014 at 10:58 AM
We can buy something that reliably supplies future services. The US national highway system was great investment. Because good investments increase the size of the pie, we don't care as much that we all can't increase our share of it.
We can invest in anything at its real net present value, but investments in things that depreciate quickly need to be rolled over, which requires investing the returns. The diligence cost and risk involved make this kind of investment problematic.
With infrastructure investment the service life is long, and it's the government's responsibility to rollover the investment (like improving roads and repairing bridges).
The principal seems clear enough despite practical difficulties.
The only investments on a macro scale are this pie increasing kind or hording. Paygo is a trap, given unfavorable demographics. Like, say, the social security trust fund. Somehow people don't see the problem with the government making proportionately large investments in its own bonds.
Posted by: Peter N | March 10, 2014 at 10:59 AM
I mean "worked in" just as in the sense of broadening out the accounting approach.
Even though you depart a lot from a NIPA straight jacket for example, your approach does include accounting consistency in a more general or conceptual way, and I think you intend that.
Just saying not to sell NIPA too short when there are complementary rather than conflicting analyses available.
Posted by: JKH | March 10, 2014 at 11:02 AM
I should probably have said "future services that increase the net present value of the economy."
The idea seems clear enough but an exact definition is tricky. Any investment to some extent affects the value of other investments.
Posted by: Peter N | March 10, 2014 at 11:07 AM
"Does this doubling of the price of land give them a better standard of living when they retire and sell their land to the next generation? Yes, but only if the next generation also doubles its saving too."
The standard of living is determined by the consumption of goods and services - here wheat. If production of wheat per land unit does not increase, the rise in the price of land does not translate in a higher standard of living. Doubling the savings will only lead to higher wheat prices or higher monetary wealth (essentially paper gains) but not more food for consumers.
"The only feasible investment vehicles are: storing wheat; building robots (labour-saving capital goods)."
Totally agree. A society can only "save" for the future by non-consumption of storable goods and investment in future productivity (I would also include education, healthcare etc. not just machines). Monetary savings will affect price levels but not directly determine if we have the goods and services we desire in the future.
Posted by: Odie | March 10, 2014 at 11:19 AM
1) "Storing wheat is a form of investment that has a zero real rate of return."
Not necessarily. If something increases the ratio of labor inputs to wheat outputs over time, then the real price of wheat may rise over time, and storing the product may have a positive real rate of return. Climate change (think the biblical story of Joseph) and population growth (within a diminishing returns to labor framework) could drive this effect. I admit, I may just be quibbling here.
2) This thread of posts has been thought provoking (esp the point about the "retirement revolution") but I wonder how far this goes beyond basic economic concepts. Econ 101 says the real rate of return of income producing assets is a function of demand for capital (cohorts looking to consume in excess of current production, investments in machinery) and supply of capital (cohorts looking to save for retirement or other purposes by consuming less than their income). What is the nuance you are looking to add to this?
Posted by: louis | March 10, 2014 at 11:21 AM
Peter N: I see long lived infrastructure investment (like roads) as a hybrid between buying land and storing wheat. It may give a better rate of return than storing wheat, but only if the next generation is willing to pay the old generation for the roads. (And maybe the next generation won't, or all drive flying cars, or sit at home playing videogames on their smartphones.)
Odie: Did you actually read and understand that bit from me you quoted? If the land doubles in value, ***the old*** get to consume twice as much wheat when they sell the land. Of course it doesn't increase aggregate wheat consumption.
No more comments on this post. Like the last time, you are wasting my time by trolling.
louis: Yep. But if wheat is the only consumption good, the real price of wheat is necessarily one.
"What is the nuance you are looking to add to this?"
Nothing much. Just the OLG aspects, which tend to get missed in ECON 1000. Land for example doesn't work as an aggregate savings vehicle in a model with infinitely-lived agents.
Posted by: Nick Rowe | March 10, 2014 at 12:06 PM
Nick--What are we assuming about population growth here? Does it matter if population is constant? Growing at 1% per year? (Or faster.) Declining? What are we assuming about TFP? Or does that matter?
Posted by: Donald A. Coffin | March 10, 2014 at 12:51 PM
"But if wheat is the only consumption good, the real price of wheat is necessarily one."
Does that exclude leisure as a consumption good? If a bushel of wheat takes an hour to produce in 2000 and two hours in 2050, isn't there value in a time machine that trades 2000 wheat for 2050 leisure?
"Land for example doesn't work as an aggregate savings vehicle in a model with infinitely-lived agents."
That is a good point. So to generalize: in Econ 1000, aggregate savings vehicles are only those that increase future aggregate consumption possibilities - new production goods, inventory, and loans to foreigners. And with OLG, we start to care about aggregate savings for a sub section of the population, for whom land, existing machinery, and even certain ponzi schemes become valid aggregate savings vehicles, so long as they are followed chronologically by another group of similarly minded savers.
Posted by: louis | March 10, 2014 at 12:59 PM
Donald: Total Factor Productivity growth and population growth may affect the rate of return on investment. They will affect the rate of return on holding land too. Presumably, both TFP and population growth would have a positive effect on both rates of return.
Posted by: Nick Rowe | March 10, 2014 at 01:02 PM
louis: fair point about leisure. A real rate of return/interest is a nominal rate of return minus an inflation rate. But *which* inflation rate? We normally assume the CPI inflation rate. But the wage inflation rate (inflation rate on leisure) is an equally valid candidate.
Posted by: Nick Rowe | March 10, 2014 at 02:29 PM
In one sense all methods of allocating resources to the non-working olg are PAYGO systems. You can only transfer what is produced or has been stored.
What is interesting is how the way the system is setup will affect both the size of future transfers and the size of future output.
In a traditional society or a system where pensions are paid for out of current taxes then people (willingly or unwillingly) simply give up some of their income in order to pay for others to consume. The advantage of this system is that (as long as people have faith in the future of the system) they don't need to worry about saving for their old-age. The dis-advantage is that people may save too little and there will insufficient investments in capital goods and the "total pie" will be grow relatively slowly thru time.
Many modern economies are moving towards a model where individuals have to "buy land or store wheat" to enable them to consume in their old-age. Other things equal storing wheat seems inefficient and buying land is just a way if achieving through ownership means what other PAYGO systems do thru tradition or fiscal transfers.
Whichever system is used I think we can distinguish between:
- A system for distributing what is available in the present that enables consumption to be shared between the working young and the retired old.
and
- A system for distributing what is available in the present that enables available resources to be shared between consumption in the present and investment that will increase output in the future.
These things are linked but somewhat distinct in my opinion.
Posted by: The Market Fiscalist | March 10, 2014 at 02:45 PM
"only if the next generation is willing to pay the old generation for the roads."
I got plenty of benefit from I91 and I95. I'm already ahead. If the ROI is positive in 20 years, everyone (on average) less than 45 at the start will be ahead. Why should the young not want to invest?
Now if you're proposing something like the Sagrada Familia, that's different (finished in 2026?)
Posted by: Peter N | March 10, 2014 at 03:19 PM
"The value of each cohort's land when it retires depends not on how much it saves, but on how much the next cohort saves."
Or another way of looking at it is that all the retired cohort gets to consume is what the working cohort don't wish to consume itself - the leftovers. All that matters is how much each individual retired has saved relative to retireds as a whole, because that determines his share of those leftovers.
Posted by: Nick Edmonds | March 11, 2014 at 06:44 AM
Even if the next generation doesn't want to buy the machines, they still help produce wheat.
The land will help produce wheat regardless of what was paid for it.
The machinery constructed today increases the future output (of wheat?) even if the future generation has no interest in replacing it when it wears out.
Of course, maybe it won't help produce wheat after all. There is risk with investment. But that risk isn't the same thing as a requirement that future generations want to save as much as the current generation.
Suppose you need a variety of goods in retirement, but just store up one good. Well, output today is available to consume in the future. But if the particular good stored is one that no one wants in the future, then it is a loss.
Posted by: Bill Woolsey | March 11, 2014 at 08:02 AM
Nick Edmonds,
"Or another way of looking at it is that all the retired cohort gets to consume is what the working cohort don't wish to consume itself - the leftovers"
If you have no role for capital, maybe. But if retired me owns the land and working you wants to farm it, you can expect to be charged rent.
As things work now, the old supply most of the capital; the young supply most of the labor. What is the size of labor's share and why? If the young don't buy capital services, then don't they have to rent them?
And is it really possible for the next cohort to not invest. Assume they don't. What exactly happens? If saving = investment, then their savings are 0 and consumption is 100% of income. How, then are the consumer goods produced, if the old are dis-saving and the young are not investing. Wouldn't production of capital goods be negative?
Posted by: Peter N | March 11, 2014 at 10:25 AM
Peter N
You're right. I was only looking at the change in value, rather than the capital share of income.
Posted by: Nick Edmonds | March 11, 2014 at 10:46 AM
There's a lot of talk about how companies are borrowing (or investing less of their operating cash flow, same thing) to return money to shareholders through buybacks and dividends. Meanwhile overall market cap seems to be rising, even net of this return of equity capital. Is this simply "land" prices (enterprise values) rising across the board and companies resetting the debt/equity mix at market prices?
Posted by: louis | March 11, 2014 at 11:06 AM
@Bill Woolsey: I left a short off topic question for you on your blog having to do with MOA and UOA.
Posted by: Tom Brown | March 11, 2014 at 12:47 PM
Being the original emailer, I'd like to say/contribute my take on this. My background is law and policy, emphatically not macro, so I'm pretty sure I'm going to make some noob mistakes.
When Nick "starts over" he says:
"Young people are working and earning an income from producing goods. They want to retire (stop working) when they are old, and yet continue to consume goods. How can they make this happen?"
This is actually not my question but I think it is a good place to start. I believe that in a situation of stable demographics the "efficient" answer to this question is that different generations in different stages (children, young adults, middle aged, old) trade preferences for consumption over time in an exchange that does not involve any net savings at the macro level, e.g., in the sense of "storing grain," although it is possible that some these exchanges might look like "buying land." Instead, if the right institutions exist, generations simply trade productivity over time.
What are the "right institutions?" They could be, in an idealized world, contracts between individuals -- "I will give you some of my (extra) grain today in exchange for your promise to give me some of your (extra) grain tomorrow (when I'm retired)." I think that a more or less Coasian analysis has led modern industrial/post-industrial countries to "institutionalize" this exchange in social insurance systems.
In this equilibrium there is no net savings at all -- just an exchange of current productivity over time. It depends on there being a surplus (in a strictly subsistence economy no one could retire). The "institution" (contracts of social insurance) depends on a sort of "faith" between generations (that we see is under constant attack -- "Social Security will not be there when I go to retire"). And it depends on some reasonable stability in demographics.
In this equilibrium condition I see no reason why the person deferring consumption should be entitled to a return ("interest"). It may be there is a "natural" imbalance between time preferences -- more people always want to spend money now than want to spend it later (when they retire) -- which may explain why the "mere" deferral of consumption "expects" a return (interest). But I can imagine situations (we may be in one; Japan may also be an example) where more people wish to defer than to spend, where the returns to deferral may be negative.
In this equilibrium condition "investment" -- defined as "producing more means of production" -- is exogenous to this retirement "savings" transaction and the returns to investment are entirely a function of the productivity of the investment; they are not a function of the transfer of consumption across time/generations.
My question, which I'm still kind of scratching my head about, is what does it mean to tell everyone to "save more?" My first answer is that in equilibrium, that is a stupid exhortation (kind of by definition, since you're in equilibrium). I think. All that it will do -- in my little model -- is distort (in the favor of one generation) the economics of the transaction that is already in place. The people deferring consumption will get a worse deal and the people consuming will get a better one than would be the case in a "natural" equilibrium. More practically, nobody should be buying more bonds right now.
On the other hand, "saving more" may make sense if the demographics have disrupted the equilibrium of this model. I'm still trying to think through what "saving more" in this context means. But provisionally, to me, it means either (1) storing grain or (2) "investing" in companies that build elder care robots.
In this context, storing grain seems like a less-efficient way of transferring surplus across generations than the equilibrium model I proposed. Less efficient because, to store grain, at a minimum, you have to build a silo. Your society/economy is forced to take this less efficient option because there isn't an adequate demographic flow to support the simpler/cheaper exchange across generations. In this simplified version returns to this "saving" should be less than zero (the silo has to be paid for). This silo-building-plus-grain-storage could be thought of as an "investment." It does enhance the ability of a single generation to transfer consumption across time.
Investing in an elder care robot may, in this context, be a more "efficient" way to provide for the future -- although this strategy involves some (maybe a lot of) speculation -- what if you build the wrong robot (the betamax robot)?
Of course, the ultimate investment/saving/solution to this problem would be to have more children. But that is obviously begging the question.
Posted by: Michael Barry | March 13, 2014 at 11:42 AM
Michael - telling people to save more can mean three things:
1) the comments are really directed not at "everyone" but solely at people working now, based on the fact that many people undersave during their working years relative to the standard of living they want to maintain during retirement
2) In a closed economy, where investment drives future growth in productivity, the less of their income people consume, the more is available to invest. By the simple Solow growth model, higher savings rates today mean a richer society tomorrow.
3) In an open economy, increasing national net saving means increasing net exports and accumulating financial claims on other nations.
Posted by: louis | March 13, 2014 at 04:37 PM
louis: I understand the basic model here. Apropos 2), I wonder what it means to "invest" more in the context of declining demographics. Is my notion that the supply of investments/new ideas goes down in that context, as the demand for investment goes up, too mystical? That is, I would say that option 2) may produce rapidly diminishing returns.
I would also suggest a fourth alternative (although this is somewhat fighting the hypothetical): have more children. I suppose that can be regarded as an investment (of course, in the US nowadays any government spending program is characterized as an "investment" -- I mean here, an actual investment). Also, way easier said than done.
Apropos 3), another alternative would be to import more people (more immigration) -- this seems to me to be the complement of exporting more goods.
Posted by: Michael Barry | March 17, 2014 at 10:24 AM