Does saving count towards GDP?

Here's a fun one. (OK, I think it's fun, anyway.) Especially for those who teach macro.

A first year student emails me. Paraphrasing, he asks "For a closed economy, we know that national saving equals national investment, and investing in newly-produced goods counts towards GDP. And "saving" means anything we do with our income other than paying taxes and spending on newly-produced consumption goods. So if I take $100 from my pay and stick it under the mattress, does that count towards GDP?"

Your instinct is to answer "No!" of course. But you should be able to see his logic.

Let me restate his question in a different way, so "saving" refers to private saving, and for an open economy, so saving is not necessarily equal to investment.

It is a national income accounting identity (i.e. it is true by definition of the terms) that:

C + I + G + NX = Y = C + T + S

[Consumption+Investment+Government spending+Net eXports = GDP(income) = Consumption+Taxes+Saving]

The normal way to measure GDP is to add up all the terms on the left hand side of that identity (the "expenditure" method). So if you were adding up C+I+G+NX, and then found you had missed $100 in I, and re-did your calculation, your estimate for Y would be $100 bigger than your original calculation.

But suppose instead you decided to measure GDP by adding up all the terms on the right hand side of that identity (we don't have a name for that method, because nobody does it that way, AFAIK). So if you were adding up C+T+S, and found you had missed $100 in S, and then re-did your calculation, your estimate of Y would be $100 bigger than your original calculation.

[And the reason nobody measures GDP that way is precisely because "saving" means literally anything you do with your income except buying newly-produced consumption goods or paying taxes. It includes: buying a newly-produced investment good, buying land, buying a used car, buying financial assets, and sticking $100 under the mattress. So it would be much simpler just to ask people what their income was.]

The problem is this: If Y = X + Z, and we ask "does X count towards Y?", we are making an implicit assumption about whether or not Z stays the same. The number of my Kids equals the number of my Sons plus the number of my Daughters. K=S+D is an accounting identity. Does "if I have one more son" mean "if I have one more son and the same number of daughters" or "if I have one more son instead of having a daughter"?

We tend to read "If I put $100 under the mattress" as "If I put $100 under the mattress instead of spending $100 on newly-produced consumption goods." But we could equally well read it as "If I put $100 under the mattress instead of taking the day off work and earning $100 less".

But "if I buy $100 more newly-produced investment goods" has exactly the same ambiguity. Instead of doing what?

I think the lesson to be drawn is that we must always specify what the alternative is, and what else is assumed constant, so we answer the question: "instead of doing what?". It then becomes as trivial as playing with words should be.

Whenever anyone says "Y=C+I+G+NX, therefore if the government increases spending, GDP will rise" I will reply "Y=C+T+S, therefore if the government increases taxes, GDP will rise."

There must be a better way to teach national income accounting.

Comments

[louis]

C + T + S represents the disposition of income, not its generation. The $100 under the mattress is counted as GDP when it was paid in exchange for the student's labor, regardless of whether he later saves it, spends it, or drops it down a sewer.
I could say a company's cash flows to equity are equal to its savings plus its dividends plus its share repurchases. That's intuitively a weaker, less meaningful statement than saying that cash flow is revenues less cash expenses plus net financing. Changing the revenue line will change cash flow. Changing the dividend line will not.
GDP recognition seems similar to revenue recognition. It happens when someone pays someone else for a good or service.

[Majromax]

Like so many other fields, I think this is a case where money confuses things.

Look at the expenditure side of GDP, but pretend we haven't invented money yet: GDP is the net quantity of stuff produced in an economy. Fix this definition into our minds, and look at where we go from there:

When we add money and have a monetary exchange economy, we can look at GDP by money flows. Here, instead of needing to add together apples and goats, we just add together the money exchanged for those. That gives us our income view of GDP, where we add together all money exchanged for work.

So, is the $100 "included" in GDP? Yes. It was given to our mattress-saver in exchange for his or her labour, so it is unequivocally included in the measured GDP. The same would be true if the saver were instead in an unfortunate accident where the $100 were burned in a fire.

Would GDP be higher if – once given – the $100 were put to some other use? Also yes, because it would be exchanged for some other product of labour. This would happen either directly in the form of consumption or a newly-produced investment good, or it would happen indirectly if the money were exchanged for an existing capital or durable good and the new owner of $100 had to put it to some use.

Now, that "yes" above is only true given an infinite time horizon. If I measure GDP on a per-hour basis, then having money under my mattress is the same as having money in my pocket on the way to the store. But we can look at this in a statistical sense with the expected chance that, given $100 burning a hole in a pocket or mattress, it will be exchanged for new production. This chance is of course related to the velocity of money.

[Nick Rowe]

louis: "C + T + S represents the disposition of income, not its generation."

True. I like that. And C + I + G + NX represents the disposition of output, not its generation.

Majro: I was really with you up to this bit:

"Would GDP be higher if – once given – the $100 were put to some other use? Also yes, because it would be exchanged for some other product of labour. This would happen either directly in the form of consumption or a newly-produced investment good, or it would happen indirectly if the money were exchanged for an existing capital or durable good and the new owner of $100 had to put it to some use."

No. Here you are making a substantive statement about the world (implicitly assuming a monetarist/keynesian short run model). None of that follows from national income accounting identities. Maybe production of apples is fixed exogenously. Maybe this guy is so unfashionable that when he buys apples everyone else decides to stop buying apples and store their money under the mattress. (And GDP is GDP regardless of whether it is produced by *labour*.)

[Majromax]

> No. Here you are making a substantive statement about the world (implicitly assuming a monetarist/keynesian short run model).

I'll admit, I was assuming market clearing behaviours with ordinary goods, where spending at the margin either induces new production (such as by employing a service worker that would otherwise be idle) or increases prices in auctions for produced goods. This would not hold in Venezuela, where the stores are out of product no matter how much money you show up with.

Some sort of substantive statement about the world is necessary for the accounting identity to be meaningful. The least surprising one is to assume that, save for our topic of whether the $100 is stored under a mattress, the remainder of the economy is in general equilibrium and the $100 affects it only on the margin.

Just as with unfashionable apples, we'd get similar surprising results of the $100 were spent on caltrops to prevent others from driving to work.

> And GDP is GDP regardless of whether it is produced by *labour*.

I don't mean to sound like a labour-theory-of-valuist here, but isn't this necessary? Production functions have labour as an integral component, even if that labour is as trivial as someone pressing a button to start robots operating. As far as I am aware, that's how we define "product."

[Nick Rowe]

Majro: "produced" goods is a little bit fuzzy, but I don't read it as meaning "produced by *labour* (with or without the help of other inputs)". Hard to think of an example where labour wasn't involved at some point in the past, but the services of capital goods, or land, might not need any labour this year.

[Majromax]

Okay, I can believe that and withdraw my "by labour" restriction as overly picky, especially since I also make arguments about time-slicing.

The thought experiment that convinced me was a vending machine: the sale of a package of chips in a vending machine is a positive contribution to GDP as inventory (the chips-in-machine) is transformed to consumption (chips-eaten-by-me) at a profit, yet at the moment of transaction no labour is involved in the supply. If we measure GDP on an hourly basis, that looks like labour-free production.

[Nick Rowe]

Majro: On an hourly basis, since that bag of chips was produced last week, and was a reduction of inventory (negative investment) nothing happens. C up $1 and I down $1.

[J.V. Dubois]

"I think the lesson to be drawn is that we must always specify what the alternative is, and what else is assumed constant, so we answer the question: "instead of doing what?". It then becomes as trivial as playing with words should be."

That or we can use different word for "Saving" that is not the same as a word that in general vaguely means "setting aside some money". Or if economists cannot help but use it, maybe they cam latin translation instead? Something like "national salvificus"? Maybe then people would actually look into the definition - and most importantly into difference with "saving" instead of assuming things.

[rjs]

C + I + G + NX = Y = C + T + S may be an accounting identity, but i dont think that C + T + S have anything to do with what we want know about GDP, given that at least as the BEA describes it, is "the real output of goods and services produced in the US"
notice that definition is not a monetary definition, it's a definition of output, and the current dollar value of C + T + S says nothing about that...
if you look at the full pdf for US GDP, you'll notice that table 3 is the only place where current dollar values of GDP come into play:
http://www.bea.gov/newsreleases/national/gdp/2016/pdf/gdp4q15_2nd.pdf
and that table is split into two sections, the second and only relevant section of which is in chained 2009 dollars, which aren't really dollars at all, but a representation of the relative quantity of goods and services produced in the quarters and years cited, which are arrived at by adjusting the current dollar values of the components with the quantity indexes shown in table 5...thus GDP is a measure of the relative change in the units of output of goods and services, and your "savings" has nothing to do with that...nor can you use dollars to increase GDP in any way; neither tax rebates or helipcopter drops of dollars will add a bit to GDP, because money does not increase goods or services until it is spent...

[Matt Youngh]

Savings is cash management, it is about 1% (a vague guess) It includes bank sellers, armored car drivers, ATM machines, vaults and buildings.
Find out the contribution savings to GDP by ucounting your ad hoc ATM fees over the month.

Depending you where we draw the line, the rest can be attributed to financial services; analysis, default risk insurance, and regulatory costs. Financial services earn about 10% of GDP, I cannot see why we should count that as cash management. And putting digits into the on demand savings account is not financial services.

[Andrew_FL]

Nick, isn't the real issue here that the question is asking for a one period answer to an implicit two period question? His income that he puts under a mattress counted towards GDI when it was received by him as income. It will not count as someone else's income next period if he does not remove it from under the mattress and spend it. Isn't the answer to his question "Does it count towards GDP?" that "It already did" and "It won't in the future"?

@rsj- In national accounts, Gross Domestic Product is defined as equal to Gross Domestic Income, so GDP may have "nothing to do" with C+T+S but it's exactly equal to C+T+S. By definition.

@Majromax-"Look at the expenditure side of GDP, but pretend we haven't invented money yet: GDP is the net quantity of stuff produced in an economy. Fix this definition into our minds, and look at where we go from there:"

I'm sorry but that's pure gibberish. You can't add up the net quantity of stuff. Stuff isn't just a homogeneous goo of "product" that can be measured in, what units would you have in mind exactly? Widgits? Utils?

There is no concept of GDP without money. You cannot add up stuff. You can add up transactions, and weight them by prices. You cannot add together the things that were traded.

Sheesh they really need to stop teaching people to think of GDP as real first, nominal second, given how completely rear end backwards that is.

@ No one in particular, much of the confusion over "savings" macro economically speaking seems to stem from the fact that what the national accounts mean by "savings" is something very different from what ordinary people think of as the object of the act of deferring consumption.

[Market Fiscalist]

'We tend to read "If I put $100 under the mattress" as "If I put $100 under the mattress instead of spending $100 on newly-produced consumption goods." But we could equally well read it as "If I put $100 under the mattress instead of taking the day off work and earning $100 less".'

It strikes me that it is always the act or working/not-working that affects GDP not the act of saving/not-saving. (Assume that every act of spending triggers an act of working as far as GDP is concerned)

"If I put $100 under the mattress instead of spending $100 on newly-produced consumption goods." is entirely about savings/not savings, and (other things equal) has no bearing on GDP.

"If I put $100 under the mattress instead of taking the day off work and earning $100 less" is about both saving and working, but only the decision as whether to take the day off or not is relevant to GDP, the other bit (How that extra day of production affects consumption and savings) is about saving/not-savings and is irrelevant to GDP.

Of course if I think something like "I want to increase my wealth by $100 therefore I will work an extra day and save everything I earn" then the increase in GDP is actually driven by the desire to save - but I do not think that means we can say "savings adds to GDP" - the work and the savings are still 2 different things.

[Market Fiscalist]

I suppose I am assuming that "If I put $100 under the mattress instead of spending $100 on newly-produced consumption goods." equates to those newly-produced consumer goods getting produced anyway, and (on account of them not being consumed) being I rather than C.

[Andy Harless]

Saving is an awkward concept to begin with. How about:

"So if I take $100 from my pay and stick it under the mattress, does that count towards GDP?"

No, because you didn't save it when you stuck it under the mattress; you just changed the location of your existing savings. You saved it when you took it from your employer's hand. And at that point it did count toward GDP, because you're employer was investing or consuming.

If you make the time frame small enough, anyone who receives income is saving it, and that is offset by investment or dissaving on the part of whoever pays it (unless the payer is a foreigner, of course, in which case it's offset by net exports).

[Nick Rowe]

JV: "That or we can use different word for "Saving" that is not the same as a word that in general vaguely means "setting aside some money"."

And Andy: "Saving is an awkward concept to begin with."

Yep! My old post on why "saving" should be abolished!

[JF]

NIPA is retrospective. That is why Identity equations, well, have cloture, in this defined and self-contained, looking-backward world.

Use of a retrospective, cloture-valid system for depicting what did happen, it is problematic when you start to look at things that are happening now or in the future. Gives insights, sure, but.

My best example of misleading points comes from the accepted NIPA-equation that I = S works looking-backward, as the terms are defined in NIPA. But this NIPA-notion is NOT, absolutely not, a rationale for public policy on taxation to favor the formation of savings, as if this savings are the font of Investment we will see, future tense (lobbyists tell people that so if we don't favor savings we are shooting ourselves in the foot and will harm the level of capital invested).

If almost everyone puts their personal savings from the prior period under the mattress, particularly in Europe where financing is done predominantly by banks, you can still see Investment in the next period as these banks can help you leverage some modest amount you have accumulated - even at 30 or 50 to 1 leverage (if you want to replay the recent financial crisis), pointing out of course that in the aggregate the coming level of Investment is not an identity with savings in the prior period.

JF

[Marko]

" There must be a better way to teach national income accounting. "

There is , using a Haig-Simons definition of income. There's no question about accounting for that $100 when you use H-S income , or C + d(NW)/dt , i.e. consumption plus change in net worth. All savings get accounted for as NW , whether invested in a new factory or stuffed in your bra.

There's an obvious explanation for our failure to use this more sensible accounting construct - it would expose the excess wealth hoarding of our ruling class , which occurs at the expense of the consumption side of the economy , where the great unwashed derive their utility. The elite don't need that headache , so don't hold your breath waiting for that better way to teach.

[louis]

JF - there's a clearer intuition to why I = S than just the accounting identities. S is income that is not consumed in the current period; it is the fraction of society's productive capacity that goes to increasing future production potential. So in a closed system, with monetary policy maintaining GDP at potential, there is a direct tradeoff between consumption and investment. Factories can build more cars or more robots.
Leverage in the banking system is irrelevant, whether you put your money in the mattress or the bank or the trash is irrelevant. If people in aggregate choose to consume less in this period, they free up society's resources (through the channels of lower prices or lower interest rates) for more capital investment.
That doesn't necessarily mean that taxes should incentivize savings over consumption. But there is a tradeoff there.

[Majromax]

@Nick Rowe:

> Majro: On an hourly basis, since that bag of chips was produced last week, and was a reduction of inventory (negative investment) nothing happens. C up $1 and I down $1.

Inventory is booked at retail prices? I was under the impression that it would be on the books at wholesale prices.

The bag of chips in the vending machine counts as $0.50 of inventory. When I purchase it for $1, consumption goes up by $1 and inventory goes down by $0.50 for a $0.50 contribution to hourly GDP.

[Nick Rowe]

Majro: I always get muddled by the retail/wholesale/indirect tax business. I pretend it's all the same.

[Tel]

I'm sorry but that's pure gibberish. You can't add up the net quantity of stuff. Stuff isn't just a homogeneous goo of "product" that can be measured in, what units would you have in mind exactly? Widgits? Utils?

Gosh, that is a problem... but seems that inventing money does not make the problem go away. For starters, not everything might exchange for money. Perhaps 90% of your economy consists of transactions with a currency component, but 10% may consist of swaps, gifts, broad agreements to cooperate (for example allowing right of way on private property instead of changing a toll), or various other shared resources.

But even if we presume that all transactions involve money, we still don't have fixed prices, nor do all people value money in the same way, nor for that matter do all people feel the same way about what they buy (some may think that $100 for a pair of shoes is excellent value and they would have paid more, while other may still buy the same shoes at the same price but only feel they got so/so value).

In short, adding up the monetary side of transactions is no more "real" than adding up the total amount of "stuff" in a barter economy. It's all hand waving.

[Henry]

Nick,.

You say saving includes..."buying a newly-produced investment good, buying land, buying a used car, buying financial assets, and sticking $100 under the mattress."

I would say:

saving = buying a newly produced investment good

dishoarding = buying land, buying a used car, buying financial assets

hoarding = sticking $100 under mattress.

[Henry]

"The bag of chips in the vending machine counts as $0.50 of inventory. When I purchase it for $1, consumption goes up by $1 and inventory goes down by $0.50 for a $0.50 contribution to hourly GDP."

I agree with Majro.

Y = C + I

I = change in inventory + change in capital stock

change in capital stock = 0

Hence,

I = 0 - 0.5 = -0.5

So,

Y = 1 - 0.5 = 0.5

Also,

Y = Wage Income + Profit Income

Wage Income = 0 in this case

So,

0.5 = 0 + Profit Income

That is,

Profit Income = 0.5

That is, the change in GDP results from the profit earned by an enterprise.

[JKH]

Nick,

Some points I would emphasize:

I think it’s more effective to illustrate this first with the very simplest closed model without government, which is:

Y = C + I = C + S

The other sectors are relatively simple adjustments after this basic conceptual form

Both sides are representations of income

S is income not consumed – it’s defined as a residual rather than a specific “destination” of money or anything else - don’t clutter it with what happens between the point where the income is measured to have been saved rather than consumed, and what the balance sheet looks like after that at the end of the same time period over which income is measured. Separate the idea of the non-consumption of income from the result for the balance sheet. In fact, the basic definition of saving as an income residual specifies absolutely nothing about what happens to the balance sheet. You’ve listed a bunch of possible balance sheet outcomes, which is fine.

An important point: macro S consists of the sum of a lot of micro positive and micro negative s’s, depending on the micro drilldown of units that can save

Apart from that, the equation is like any other equation – you can only solve it for one unknown at a time. You either have to know or make assumptions about other variables apart from that. And like any other equation, you can specify the variable values at different points in time, so obviously you have to be consistent about what changes and what doesn’t during that time period. I see nothing unique about this kind of algebra in this case.

The biggest conceptual mistake I see made is this notion that an accounting equation like this is useful only as an ex post measure rather than saying anything about the future. In fact, if you accept that this accounting identity has meaning on an ex post basis, and that it has meaning in specifying the state of the world in that sense at a specific point in time for a specific period leading up to that point, then it becomes a constraint on the *specification* of possible future outcomes and states of the world for those same variables. E.g. recognizing this definitional/conceptual constraint is what all the commotion about “sector financial balances” is about in MMT and other “heterodox” thinking (btw, Goldman Sachs uses this prominently in its thinking and economic forecasting). Although, as you’ve noted in the past, sector financial balances thinking is just a rearrangement of national income variables. But with a different "flow of funds" framing for it.

[Nick Rowe]

JKH: "The biggest conceptual mistake I see made is this notion that an accounting equation like this is useful only as an ex post measure rather than saying anything about the future."

Lets add that to your previous point about the distinction between aggregates and individuals (where that distinction is at its starkest in a closed economy).

Each individual's plans and expectations for their future purchases and sales must satisfy an accounting identity for that individual, but those individuals' plans and expectations may not add up to satisfy any aggregate accounting identity. I am planning to save, but you are not planning to invest. In other words, the representative agent is planning to spend less than he expects to earn, which is an accounting contradiction, but he doesn't realise it's a contradiction because he does not know that he is the representative agent. He thinks he's a special snowflake.

Only in (expectational) equilibrium do the plans and expectations add up to satisfy the accounting identity.

This is an old Hayek (IIRC) point, and goes back to my old Steve Keen post.

[JKH]

Nick,

I think the idea that expectations are not always realized is obvious - while the idea that the accounting identity always holds in actual experience at all times is not so obvious.

It’s obvious that my decision not to get a haircut will reduce my barber’s income - compared to the counterfactual. He may have expected the counterfactual that he does not in fact realize.

It’s not so obvious that the accounting identity holds every step of the way - in the case of either the actual experience or the counterfactual.

[JF]

They add up because they are defined to add up - and they happened as the reportage is past-tense.

Look at the comment above by Louis directed back at me. His first sentence is not past-tense, it is specific to the current period, present tense - "S is income that is not consumed in the current period" - using a term defined to produce this retrospective identity with the other term Investment. These are not interchangeable' I = S, in the present or future where the terms have different meanings and definitions.

And therein is the reason it must be used with care.

To go back to my example above, the acceptance that the world operates going forward on some cloture-seeking retrospective using terms defined for cloture purposes can lead economists and the people to advise to ignore the purpose, roles and mechanisms of the financial community.

The financial community provided lots of evidence that this is a perilous view of how the world of economics actually works.

Just look at 2000 to 2007. My related example is for people to look at the magnitudes of the financial asset trading marketplaces, comparing just the year 2000 to the year 2007. Just looking at BIS Over the Counter (OTC) derivatives stats, you find 2007 the values are over $700 TRILLION but less than 10 years earlier it is two orders of magnitude less. How can these financial positions come from personal savings accumulated in the prior period, they are not accumulating by not consuming, not at these rates of change (the 'money' clearly comes from somewhere else to back these 'Investments')? These facts, and they are reported from what happen, should set off alarm bells -- does it not?

[Nick Rowe]

JKH: "It’s not so obvious that the accounting identity holds every step of the way - in the case of either the actual experience or the counterfactual."

True. The accounting identity holds in all possible worlds at all times. But the accounting identity does not hold if we aggregate over individuals' planned future purchases and sales. Each individual expects a different possible world. Their aggregate plans cannot be carried out in any possible world. Those plans are mutually inconsistent.

[Majromax]

I think it also helps to remember that the 'I' part of 'S=I' includes unwanted investment in inventory. That's obvious from an accounting perspective, but too often rhetorically we think about "productive investment."

@JF: Never, ever look at the notional values of derivatives, which is what you're doing there. They do not represent any form of wealth, since derivative contracts have much smaller market values than their notional value -- they're based on the change of a security's price from some baseline.

For that matter, stop looking at securities prices in general, because securities aren't money. If I own land, the on-paper value of that land could balloon from $1/acre to $1mil/acre based on what my neighbours would be willing to pay for it, but that increase in unrealized wealth does not require an act of saving or consumption on anyone else's part. "Savings" in the context of this thread means strictly what happens to cash that was once in your pocket.

@Nick Rowe:

> Each individual expects a different possible world.

If we're considering hypotheticals, I don't think each individual envisions an entire possible world – just the part that directly affects them. Economic paradoxes (paradox of thrift, bubbles) happen when the errors in individuals' partial expectations are strongly correlated by interactions.

[Roger Sparks]

JKH: When you write "I think it’s more effective to illustrate this first with the very simplest closed model without government, which is:

Y = C + I = C + S",

I think you are correct.

I would put a different spin on the I and S terms however.

We are all aware that an increase in bank lending is expected to cause an increase in spending, causing an identical increase in GDP. An increase in bank lending (is by accounting) money that is not repaid to the bank. Money that is not repaid to the bank becomes someones savings. Therefore, we can relate the term "I" to an increase in investment (from the bank's perspective) and we can relate the term "S" to an increase in savings (which may go under the mattress). I and S would be the same thing.

[Market Fiscalist]

It is definitely true that if C and T stay the same and someone saves more then GDP will have increased. But they can only succeed in saving more (if C and T stay the same) if there is a corresponding increase in investment, the government defect, or the gap between exports and imports,

[JF]

@Majromax - 1) I am very familiar, having done tax policy for decades, with notional vs. contractual understandings of the payments tied to derivative contracts. You missed the point about explaining where the excess money came from to cover the explosive, but short-period, of growth in financial asset marketplaces. Does this not cause people to ponder about the use of NIPA-retrospectives? 2) To take your land example, it must be true that the stupid neighbor who is willing to pay $Million for something you expended $1 must have Saved that $Million first (otherwise you are really making up a hypothetical), if it is real then they must have Saved all this money (from this period, from last period, from all of the prior periods, including from bequests).

DeLong had a column about a year or so ago using the term Thrift to refer to the fact that people save money from their income for some purpose, and that society wants this to occur. But it is not just for investment purposes. Nick Rowe was absolutely right in the 2012 blog-thread, we need different terms and we end up confusing (and I've said this has been used intentionally to mislead about public policy, which is ugly, really).

I can't fight the NIPA cloture rules and definitions, though I must admit I've suggested that under a new democratic administration the BEA start to introduce different terms, and re-state the series using them. And they would do that with an upfront explanation the the term savings has been misused, being equated with capital investment potential in the present and future economies, and the series is being introduced to correct this, so it is not incorrectly used to support public policy about thrift, about capital formation, about investments, including taxation policy.

So Nick Rowe, agree? Should BEA and all other NIPA reporters in the world update their reportage using better terms and new introductory explanations?

[JF]

And Roger Sparks is pointing out how a bank establishing a lending account 'deposit' - this deposit (net of paid claims against it) is owned by the borrower. Clearly this amount was not saved from current or even past income.

The accounting that is done at the end of some period, counts it, and puts it into a defined-bucket and the accounting reports it as an identity, when looking backwards, calling the bucket either savings or investment, depending on the context of the discussion.

NIPA could use the same cloture rules, just use a different word other that the word 'savings' (or term, as I wrote above) and make sure people understand this reportage to be a retrospective, using definitions that should be understood.

Glad to see this come up again. Last post by me for a bit.

[Henry]

"But the accounting identity does not hold if we aggregate over individuals' planned future purchases and sales."

The accounting identity always holds ex poste.

However, ex ante expectations need necessarily not be realized - that's called not being in equilibrium.

For instance, S always = I but S and I need not necessarily be in equilibrium.

[Market Fiscalist]

'It [savings] includes: buying a newly-produced investment good, buying land, buying a used car, buying financial assets, and sticking $100 under the mattress. So it would be much simpler just to ask people what their income was'

If you were about to stick $100 under the mattress, but them decided to buy a newly-produced investment good (that would not otherwise have been produced) have you not increased GDP merely by changing the form of your savings ?

[Henry]

JHK,

"In fact, if you accept that this accounting identity has meaning on an ex post basis, and that it has meaning in specifying the state of the world in that sense at a specific point in time for a specific period leading up to that point, then it becomes a constraint on the *specification* of possible future outcomes and states of the world for those same variables."

Y = C + I is an accounting identity, it is not necessarily a functional relationship, it need not saying anything about future behaviour.

[Henry]

MF,

"If you were about to stick $100 under the mattress, but them decided to buy a newly-produced investment good (that would not otherwise have been produced) have you not increased GDP merely by changing the form of your savings ?"

The form of saving is not changed. You are merely saving and redirecting income flow.

Sticking $100 under a mattress is not the act of saving, it is the act of hoarding, it is the increase of a stock item.

[Andrew_FL]

@Tel-Yes. RGDP is meaningless. NGDP is not, however. It's not a measure of stuff at all, it's a crude (partial) measure of the flow of money.

[Alexander J Field]

The answer is quite simple. If you stuff $100 under your mattress rather than spending it, this will show up in the short run as an increase in unintended inventory accumulation. Whether intended or not, inventory accumulation is part of gross private domestic investment (I), and thus part of GDP.

[Nick Rowe]

Alexander: now consider an economy where all goods are services, like haircuts, that cannot be stored in inventory.

See, you are doing implicit theory, not national income accounting.

[djb]

I don't know how they decide to do national accounting

but I don't believe that the above "true by definition" identities are in fact true by definition

simplifying I plus g minus t plus c plus ex-im = y

then I plus g minus t plus ex-im is what Keynes referred to as I in his Y = I + C

so lets keep it simplified

and then you add in the accepted identity S = I

Y = I plus C = S plus C

if S, which is savings equals I, then S is simply the preservation of the original Investment

investment is that preexisting wealth added to the economy, and savings then is just the PRESERVATON of the preexisting wealth to the economy, no new wealth

so if that is true then NO NEW WEALTH is added to the economy

so where do we fit in the NEW WEALTH?

instead S = I

it is S = I plus net production

it is from net production that we get new wealth

that is newly produced wealth minus that wealth which was depleted during the time period

and why do I add it to savings and not to income?

because SAVINGS IS WHAT WE HAVE LEFT OVER at the end of the given time period

so

S = I plus net production

just preservation of the investment money plus net production

and any new net wealth created is the value of net production

[djb]

so does savings count towards GDP?

that part of savings that is preserved investment counts towards GDP because it is the same money as the investment, and investment counts towards GDP

but that part of savings that comes from net production is new wealth, and it does not count towards gdp

gdp is a measure of income

net new wealth is sort of on another axis from income,

you could have gdp go up and wealth go down, like in wars and national disasters

or you could have wealth go up and GDP go down

you could count things like nature as part of our wealth, and this goes up and down all the time, if you could calculate a value for it

though net production tends to go up if gdp goes up, because presumably a lot of the income is paid to get people to produce things

[Henry]

dgb,

"investment is that preexisting wealth added to the economy"

Investment is production of new capital goods in the period in consideration, it is not pre-existing.

"if S, which is savings equals I, then S is simply the preservation of the original Investment"

S is the diversion of productive resources to the production of new capital goods (in the simple economy described).

[Henry]

Alexander,

" If you stuff $100 under your mattress rather than spending it, this will show up in the short run as an increase in unintended inventory accumulation."

The problem we face in the discussion in this thread is confusing the aggregate perspective with the individual perspective.

On an individual basis, S is more than likely not equal to I.

In aggregate, S is always equal to I - it is a truism.

[djb]

henry,

if investment is not preexisting then where does it come from

production of new goods is facilitated by the income that results because of investment

and I am proposing that savings does not "always equal investment", that this supposed "tautology" is incorrect

if savings is that which is left over after the given time period, it includes the investment that is preserved as savings and also includes new net production

[Henry]

djb,

"if investment is not preexisting then where does it come from"

New capital goods in any period are produced by capital assets that were installed in a prior period. The production of the pre-existing captial assets formed part of the income stream in a prior period.

[djb]

new capital goods are produced by people, by transforming capital assets that either already existed or were produced in a prior period, the peoples income comes from preexisting wealth and the capital assets that were transformed existed from a previous period, ie preexisting

[Henry]

djb,

Yes I can agree that people's income in the current period comes from capital assets produced in a prior period. But you've changed your tune a little. Further above you said:

"investment is that preexisting wealth added to the economy, and savings then is just the PRESERVATON of the preexisting wealth to the economy, no new wealth"

Investment is defined as the addition to the capital stock in the current period (let's forget changes in inventory for the moment). For there to be investment, not all production in the current period can be of consumption goods. By definition, what is not consumed out of current income is saved.

[Oliver]

Alexander: now consider an economy where all goods are services, like haircuts, that cannot be stored in inventory.
See, you are doing implicit theory, not national income accounting.

What do you mean by implicit theory? Does the accounting change if what it denotes is inexistent? Or does that just mean that the accounting remains but is telling us less about the real world than we think?

Having said that, it is precisely that supposed conundrum which makes the money circuit / credit theory so appealing. If you start from the assumption that money is borrowed into existence, in this example by the person consuming the haircut, as opposed to just magically appearing, you end up with with a guy with a great hairdo, a corresponding debt but no asset to show for himself. So he'd better get working for the hairdresser to earn back the money to pay back his debt. At which point the money disappears along with the debt, saving and investment. So yes, there is an intermediate step in which S will appear without any real counterpart in this particular consumption economy. But there is also an obligation with no corresponding investment good that will tend to make it disappear again, at least in theory. One can then add investment goods, at which point the concept of saving begins to make proper sense. Or is that implicit theory again? Doesn't one need a theory to explain what the accounting means? Or what it's supposed to mean?

[Oliver]

But that's off topic, I suppose. Maybe another way to put it is that when the $100 changes hands for a new product it counts towards the flow of national income / output. In all other circumstances, including stuffing it under a matress, it shows up as a stock of S / I. The act of spending on value not previously recorded is the accounting equivalent of production.

[Majromax]

Thinking about this in some more detail, we might have a definitional issue: when does savings happen?

Imagine we have a haircut economy. Everyone wakes up to provide and receive haircuts; they pay the cash at the beginning of the day and empty out the till at the end (so the daily velocity of money is at most one, and there are no payment loops).

We can obviously measure GDP on a payment or income basis equally, as payments provided equals payments received. But if we measure GDP on a daily basis and I decide that despite receiving $10 today I'll only spend $9 tomorrow and store $1 under the mattress, when – if ever – is savings equal to $1?

Measuring GDP from midnight to midnight, in day 1 I have a consumption of $10 and an income of $10; in day 2 I have a consumption of $9 and an income of $10, but someone else has a consumption of $10 and an income of $9. (In day 3, feedback kicks in and I might not have an income of $10). Yet all of this is "C=C", not "C+I=C+S".

To take a long-term and somewhat silly view of the question: does buried pirate treasure count towards GDP?

[Ricardo Martins]

Professor Nick,

If Government increases G it will not necessarily crowd out "other demand components" (but it may), but if it increases Taxes those will have to come from C and/or S, isn't that right?

So you can say that an increase in G may increase Y, but an increase in T won't.

Am I wrong?

Thank you

Ricardo Martins (losinterest.wordpress.com)

[Roger Sparks]

(The punch line is in the final paragraph)

From the earlier JKH comment, we have

Y = C + I = C + S

where Y is simplified GDP, C is consumption, I is investment, and S is savings.

For simplified GDP we assume that private (not-Government) consumption income is equal to private consumption expense.

For this three equality equation, we have first GDP, then private income and third, private expense.

Notice that the C term does not account for all of the GDP recorded. Where did money for the excess GDP come from? It came from the I term (investment).

Of course, investment must come from a source. Some people saved their earnings from providing consumption services for others, filling the S term.

For many of us, this explanation is circular, and not a convincing answer. Inventory adjustments for production with life span greater than one year provides part of the answer. For example, housing is not expensed the year of building.

The complete GDP equation will include Government activity and exports/imports. We all know that government spends more than it receives in taxes. This excess spending is all borrowed and it counts towards GDP. In economics, we call this excess spending "investment".

But there is even more to consider for a complete explanation!

Term Y, in the macro economic view , is the output for the whole economy. When output is defined as income, we count only the money exchanged for goods and think we have a reasonable measure of economic activity. In my view, this is an error. We have ignored the change in debt which is an additional payment that the macro economy has exchanged for output. In other words, speaking from a macro economic perspective, the output achieved in a one year time period should be measured in terms of both debt and cash money; the tallied consumed goods were exchanged for money and debt .

[Roger Sparks]

Here is an example to illustrate the preceding comment:

Remember the old western movies where a drink is exchanged for a tally on a tab? No money changes hands, only a drink and debt.

Should that exchange be included in GDP? If so, would you translate the value of the debt into cash money? How do you display both the income and expense methods of calculating GDP?

[Marko]

If you think about the economy in a more comprehensive way than simply "gdp" , you recognize that there are two monetary incentives that motivate us to work : consumption and wealth ( net worth ). Then you might ask : What is the monetary funding source for those two things ? It turns out that cumulated gross savings plus domestic nonfinancial debt matches up well with the sum of current consumption plus total net worth , i.e. ~ dollar for dollar if the mean of market fluctuations of net worth is used. FRED doesn't have cumulated gross savings , but here's a log plot of annual changes :

https://research.stlouisfed.org/fred2/graph/?g=3EUf

If you plot the long-term cumulated totals as a log-log scatter plot , you get a nice linear relationship , with slope = 1 , suggesting an intercept at zero , i.e. back to when two cavemen sitting by the fire negotiated the terms of the first-ever mortgage ( on a a nice little starter cave , in a good neighborhood , with highly-rated game trails ).

[Frank Restly]

Roger,

To introduce debt, you need to introduce time into the equation.

Consumption(t1) + Investment(t1) + Government spending(t1) + Net eXports (t1) = GDP(t1) = Consumption(t0) + Taxes(to) + Saving(t0)

The first group of terms is the goods / services part - what is money spent on? This money is spent at time t1.
The second group of terms is the means by which money is obtained. Money can be income received from the sale of goods, it can be taxes, or it can be negative savings.

That is where debt comes into play. Negative savings at time period t0 becomes some type of expenditure at time t1.

[Nick Rowe]

Ricardo: "So you can say that an increase in G may increase Y, but an increase in T won't.

Am I wrong?"

I think so. Government taxes everyone, so people work more to produce more income to pay the tax. The most obvious example is corvee labour, where the tax is paid in kind, but it makes little difference in principle if it's paid in cash.

[Henry]

The thing about debt is that it is a two edged sword - there's lender and there's a borrower. In aggregate they neuter each other.

They are also stock items (balance sheet items) and not income flow items (income statement items).

Interest on debt is an income flow item. Presumably the lender is making a profit on the loan so his profit will appear in the income flow.

[Henry]

Majromax,

"To take a long-term and somewhat silly view of the question: does buried pirate treasure count towards GDP?"

I would say if left buried, no.

If retrieved, yes. Think of the expenditure incurred. This ends up in the income flow. As for the treasure itself, I would say it's like the production of a new capital good - i.e. a good that keeps giving.

[Ricardo Martins]

Professor Nick,
I would kindly disagree with you. I guess nowadays people work the amount they are offered to work, so it doesn't make a difference.
But maybe it's just my naivety.
Thank you for your response
If you have time, please read my (still enfant economics blog)

Ricardo

[Roger Sparks]

Frank R:

You write "To introduce debt, you need to introduce time into the equation.

Consumption(t1) + Investment(t1) + Government spending(t1) + Net eXports (t1) = GDP(t1) = Consumption(t0) + Taxes(to) + Saving(t0)"

I think time is already in the equation. Consumption(t1) is the consumption measured as a sum-of-transactions between measurement t0 and t1 (with a time period between the two measurements).

If this is correct, then your equation should read

Consumption(t1) + Investment(t1) + Government spending(t1) + Net eXports (t1) = GDP(t1) = Consumption(t1) + Taxes(t1) + Saving(t1)

with any t0's changed to t1's.

Any exchange that is added to GDP is an "exchange". This requires two parties for every exchange. One party receives income but the other party has an expense. GDP can be counted by either adding incomes or adding expenses.

[Henry]

Roger,

"Remember the old western movies where a drink is exchanged for a tally on a tab? No money changes hands, only a drink and debt."

No-one seems to want to have a go at this one, so I will give it try.

Presumably the bottle of whiskey was added to inventory and income in a prior period.

In the current period (when drink was provided):

Income = Bar owner's Profit = Sale of drink - value of one shot reduction in whiskey inventory

Forget the debt - it's a stock item - if there is no interest being paid, there is no income impact.

[Roger Sparks]

Henry,

I am thinking this through as I write.

As you say, when the bottle was purchased by the barkeeper, it should have been counted as GDP. The barkeeper spent money, the bottle producer received money.

We are discussing a single bottle so I doubt that GDP is aware that the bottle is inventory. Of course it is inventory in the eyes of the barkeeper.

Now an economist walks into the bar to count GDP. I think an economist walking into the bar to take GDP would begin as he walked in. This would be measurement tO. He would count a bottle on the shelf (full) as inventory but as inventory received in the prior period (before t0).

Nothing happens for a while, and then, just before the economist decides to end the GDP measurement period, recording no sales, in comes Joe and orders a drink, "Put it on the tab.". How does the economist record this transaction?

I think he would record the cash money value of the exchange as GDP. Joe has expense (which Joe calls an investment - it makes him feel better) and the barkeeper has income (a mark on the tally - which is hopefully cash-income someday).

The economist leaves, with a t1 GDP measurement of one drink exchanged for debt. He also notices that the bottle is partially full, down from full at first observation.

The challenge for the economist is to decide what to record. Should he record the fair cash value of the drink, the change in level of the bottle, the tally in the tally book, or Joe's better disposition?

Up to this point, the economist had no drinks so hopefully he put all this on the correct sides of the income/expense sides of the GDP equation. We have just enough difficulty keeping track of these concepts to make we wonder (about who is drinking what). (I hope you all smile!)

In the real economy, debt may be masked by bank lending. Joe would have plenty of money so the GDP increment would be the value of the cash transaction. The tally mark and debt acquisition would be hidden behind a bank deposit and loan document.

[Henry]

"Nick,.

You say saving includes..."buying a newly-produced investment good, buying land, buying a used car, buying financial assets, and sticking $100 under the mattress."

I would say:

saving = buying a newly produced investment good

dishoarding = buying land, buying a used car, buying financial assets

hoarding = sticking $100 under mattress."

Just need to clean something up from this post.

I would like to add to "dishoarding = buying land, buying a used car, buying financial assets", "as long as there is no profit/loss on the transactions, which if there was, would appear in the income flow".

[Henry]

Roger,

"In the real economy, debt may be masked by bank lending. Joe would have plenty of money so the GDP increment would be the value of the cash transaction. The tally mark and debt acquisition would be hidden behind a bank deposit and loan document. "

Isn't it all in the timing?

The transaction did occur. It must have an immediate income effect (and I will still argue that the income effect is reduced by the change in inventory). When the cash is received is immaterial. When cash is actually handed over, it in effect becomes a change to a stock (i.e. balance sheet) item, there is no income effect. When a business sells a good on credit, it has notionally recorded a profit and a profit is recorded in its income statement. When the cash is received to repay the credit another profit is not booked - that would be double counting. There is merely a shift between assets (credit to cash) in the business's balance sheet.

[Kaleberg]

This one seems rather obvious. Look at the transactions. He got the $100. That transaction counts as part of the GDP. If he spent the $100, then that transaction would have been part of the GDP as well.

I think some of the confusion is that people try to follow the money, but a $100 bill can be used in any number of transactions over a year. You get this problem with physics. Accounting transaction statements are like free body diagrams. If nothing changes velocity, then there is no force. If there is no transaction, there is no economic impact.

[Roger Sparks]

Henry,

You raise a valid point about the inventory change; the bottle did go from full to partly full.

The BEA (Bureau of Economic Analysis) produces a guide to national income and product accounts (NIPAs) which includes the GDP measure. This guide can be found at

http://www.bea.gov/national/pdf/nipaguid.pdf

in PDF format.

A change in inventory that is consumed is counted in GDP. To prevent double counting, the sale of the full bottle to a re-seller would NOT be counted towards GDP. Instead, the retail value of the drink (which Joe purchased) would be counted. I think the economist recording GDP would report Joe's drink as income to the barkeeper but - because there was no money exchanged - the income would be classified as "savings (S)". Joe would clearly be a consumer who reduced the barkeep's inventory but did not pay money. Joe's consumption would be recorded as an investment. Measured in this fashion, GDP, I, and S would increase but term C would remain unchanged.

The only alternative to this GDP distribution would require that term C be unequal on each side of the simple GDP/income/expense equation.

[Henry]

Roger,

" the income would be classified as "savings (S)"

Was the drink consumed or not? Are you saying it was not consumed?

"Joe's consumption would be recorded as an investment."

You have consumption and investment in the same sentence. It can't be both. Can Joe consume this drink again, and again, and again, etc.? I don't think so. (Unless of course he spits it out into a flask, then you might have point. :-) )

[JF]

If a bar owner tallied an added debt-increment this has a value as an account payable (it is a financial asset from this perspective).

The scenario is unlikely to unfold unless the drinker and the bar owner have personal relationships where the bar-owner assumes the financial risk but for no real gain - no GDP, from that perspective.

I think Roger Sparks is pointing out that the more likely scenario is the drinker who has a bank give them a loan, and then they buy a drink with some of the money. The bank's lending account is Investment. The buying of a drink is consumption by the drinker, decrementing the Savings they own in the lending account at the bank (at some time before or afterwards if they pay with a check) with the exchange being counted toward positive GDP on the bar-owner side. But the point again, is that the money came from whole cloth at the bank - it did not come from aggregate Savings as this term is viewed in a lay sense - but NIPA has defined rules allowing you to call it a decrement from Savings by the drinker, even though the savings came from nothing, and were in NIPA accounted for as an Investment (identity shows up, I decrement some bucket and in one context I call it Savigns, but in the context of why the bank established the account, it is counted as Investment - but it is the same bucket. And it is filled up with what?? Whole cloth.

Need to teach this NIPA system as it is, but make sure it is not used in a tail-chasing way to explain the present tense or the future (except as a type of depiction of the end state of the prior period).

[djb]

henry, I haven't changed my tune

investment is the addition of the preexisting wealth to the economy that goes into income which is Y

Y = I (investment) + C (consumption)

at then end of the given time period the investment, as Keynes showed, is preserved as savings "in someones pocket" if you will

so since this part of the savings is actually just the investment preserved, it then is part of income, since it is actually just the investment with we have already determined "by definition" is part of the income

there is another part of savings, if we consider savings as that which we are left with, after the giving time period

and that is net production

it does not matter where the production occurred, capital goods or durable consumption goods or public goods like infrastructure

that which we are left with should considered as savings

so wealth is in that way increased, by net production, which becomes part of total savings, or total wealth, or total capital, whatever you prefer to call it

[djb]

"so wealth is in that way increased, by net production, which becomes part of total savings, or total wealth, or total capital, whatever you prefer to call it," but this wealth increase is not part of gdp, and it should be considered as savings

[Henry]

djb,

" but this wealth increase is not part of gdp, and it should be considered as savings"

Then you are not defining "saving" as a macroeconomic accountant would. This is your own definition. Saving is not capital, it is not a stock item. In macro accounting terms it is defined as what is not consumption in the income flow.

[Oliver]

Wiki: Saving differs from savings. The former refers to the act of increasing one's assets, whereas the latter refers to one part of one's assets, usually deposits in savings accounts, or to all of one's assets. Saving refers to an activity occurring over time, a flow variable, whereas savings refers to something that exists at any one time, a stock variable.

[Henry]

Good point Oliver.

I presumed he meant "saving" given the context.

Many posts above djb says:

"and I am proposing that savings does not "always equal investment", that this supposed "tautology" is incorrect"

This suggests he is using "savings" to mean "saving".

I'm wondering now if djb means "savings" or "saving" when he says "savings"?

[Roger Sparks]

Henry,

I think we have two issues here.

1. Double entry always has two ways of defining each entry.

2. The second issue: if we have a measurement of economic activity (meaning "exchanges") occurring between two dates, we have a single measurement.

That single measurement is composed of two accounting categories, income and expense, but each (income and expense) is a proxy for the fact that an exchange (with value) has occurred.

Next consider that the producers of the GDP measurement have decided that an exchange-of-ownership-of-inventory should be counted towards GDP. The production of that inventory results in income for many people but the income frequently occurs in the prior GDP period. How do you (as the producer of a GDP measurement) do the accounting for this contingency?

I think the answer is to have the terms "investment" and "savings". This allows GDP to measure "transactions" (in terms of money) with the further breakdown into categories of "investment" and "savings" to fulfill the requirements of double entry accounting for inventory.

[vimothy]

Nick, Your example shows that (a software engineer might say) micro and macro are at two different levels of abstraction. This is somewhat complicated, so naturally it's hard at first to see how to resolve them.

[Henry]

Roger,

"The production of that inventory results in income for many people but the income frequently occurs in the prior GDP period."

I would say:

The income derived from the production of the inventory is added to GDP in the prior period. That added inventory is of course defined as investment.

All that is taken account of (i.e. added to income) in the current period (when the inventory change occurs) is the profit/loss the inventory change yields for the inventory owner. And the profit/loss = sale value - inventory change. So the sale value is added to income and the inventory change is deducted from income. If the good is a consumption good then consumption is incremented by the sale value and investment is decremented by the change in inventory (disinvestment).

"I think the answer is to have the terms "investment" and "savings".

Isn't the problem with that, that given the definition Oliver provided in a prior post, "investment" is a flow item and "savings" a stock item. GDP only accounts for flow items.

Did I understand you correctly?

[Roger Sparks]

Henry,

Before I began writing this reply, I took a quick look at BEA's guide to NIPA (referenced in an earlier comment). They use the phrase "estimates of consumption of fixed capital (CFC)". The bureau seems to have struggled with this issue continuously, changing their procedures occasionally.

Briefly, the problem of measuring consumption for cars illustrates. A car is built in one time period, sold in a second period, and resold many times over many periods. When is the car "consumed"? When is the labor used to build the car "consumed"? When is the related consumption of car and labor measured in GDP? And does the GDP increment consist of consumption or investment/savings?

You write "............. "investment" is a flow item and "savings" a stock item. GDP only accounts for flow items."

Yes, I think GDP accounts for flow items but GDP also seems to count changes in stock items. Again, a car may be the best example, but what I think is correct may NOT be the way BEA does things. So I think - if a car is built, the labor used in construction should add to GDP, increasing also the investment and savings measure. If the car is sold in a second measuring period, this should add to GDP again, this time increasing the consumption measure.

Did we double count the car? Yes, I think so. Will we double count the car again when it resells in even later time periods? Yes, I think so. Does BEA make an adjustment for consumption to reduce this double (or multiple ) counting? Yes, I think so but I don't know how they do it.

I think the breakdown between consumption and investment/savings is adequately complex to allow subjective choices. GDP is more a political measurement and less an accounting report.

[Henry]

Roger,

Regarding assets like second hand cars which can be traded, the profit or loss made by the owner selling the asset makes its way into the income statement (i.e. GDP).

Yes, I would agree that if the car was made in a prior period and not sold in that period, its cost would be added to GDP as change to inventory (i.e. investment). If it is sold in a subsequent period what is effectively booked to income (GDP) is the profit/loss (= sale - inventory change) made by the owner of the vehicle who sells the vehicle.

[djb]

well, henry, i am saying new production is part of what is left over and that gets added to the total wealth = total capital = total savings

it is not counted as income but should be counted as savings (new wealth)

it is the only way to get new wealth or new capital, call it what you want

there is an additional part of savings that is income

and that is the part of the savings that equals investment

this is not new wealth, this is simply preservation of the investment

simple example, say the investment is all currency, it does its work gets added as part of the income with consumption being the other part of income and via multiplier effect you get total income

now people do not spend all their income, they spend some, save some and at the end of the process the currency has neither been created nor destroyed, it continues to exist as "savings" "in someones pocket"

so this part of the savings, that which is the preservation of the investment, actually is the same money as the investment money and it is left over at the end of the given period as savings

but is not new wealth, so it does count as income, because it is actually the same money as the investment money which of course counts as part of income

so this part of the savings counts as income but not as new wealth

whereas the savings that comes from net production counts as new wealth but not income.... at least not part of I + g - t + c + [ex - im]

[Frank Restly]

Roger,

"I think time is already in the equation. Consumption(t1) is the consumption measured as a sum-of-transactions between measurement t0 and t1 (with a time period between the two measurements). If this is correct, then your equation should read:

Consumption(t1) + Investment(t1) + Government spending(t1) + Net eXports (t1) = GDP(t1) = Consumption(t1) + Taxes(t1) + Saving(t1)"

I am trying to get this into an equation of exchange type format (MV = PQ).

Consumption(t1) + Investment(t1) + Government Spending(t1) + Net exports(t1) = PQ : This is the goods portion of the equation
Consumption(t0) + Taxes(t0) + Saving(t0) = MV : This is the money portion of the equation

The reason I added the two different time parameters ( t0 and t1 ) was to recognize that there is a time delay ( t1 - t0 ) between when money as income is received (MV) and when it is spent on goods / services (PQ). This method allows us to recognize that income received from the sale of consumption goods at time t0 is not identical to money spent on consumption goods at time t1.

[Roger Sparks]

Frank R.,

OK, I think I understand your intent to show that income received in period one can be spent in period two.

As we have proceeded through these comments (Nick, thanks for this post!) I have become more keenly aware that GDP is intended to be a measure of INCOME and production within one time period.

If I understand correctly, the BEA is trying to get a measure of income rather than a sum of all transactions. So, to express it mathematically, let M be Money and G be all goods and labor. I (apparently) incorrectly thought GDP was the sum of the G terms in the sequence

M = G = M = G = M = G =......... (apparently incorrect)

where I show three of a much larger number of G's.

Instead, I now think that GDP is intended to be an estimate of the value of NEW production, some of which is destined to become residual inventory at the end of the period. To express this mathematically, we need the additional term NG standing for New Goods (which would include labor used in the period). Then we would have the sequence

M = NG = M = NG = M = G = M = NG = M = G = M = G = ..........

GDP here would be the sum of the NG terms, with the sum of the G terms uncounted in GDP. I think there is an adjustment in GDP for depreciation. Clearly there is an added increment of income that comes from the ownership of existing homes, an increment treated as rent.

The sequence illustrates the time delay (I think) you were trying to demonstrate. The sequence would unfold over a period of time, each using money as the exchange facilitator.

I need to tweak my (personal) estimation of the role used machinery (including used cars) plays in the GDP measurement.

[Too Much Fed]

JKH said: "I think it’s more effective to illustrate this first with the very simplest closed model without government, which is:

Y = C + I = C + S

The other sectors are relatively simple adjustments after this basic conceptual form"

I think so too.

Y = C + I and
Y = C + S

"An important point: macro S consists of the sum of a lot of micro positive and micro negative s’s, depending on the micro drilldown of units that can save"

A really important point here too.

"For a closed economy, we know that national saving equals national investment, and investing in newly-produced goods counts towards GDP. And "saving" means anything we do with our income other than paying taxes and spending on newly-produced consumption goods. So if I take $100 from my pay and stick it under the mattress, does that count towards GDP?"

JKH, let's skip the taxes. Foreign sector = 0, gov't sector = 0, private S = 0, and private I = 0. The person saves $100 and puts it under the mattress (does not invest). I believe the person is asking what happens if someone saves but does not invest and no other entity invests. Private I = 0, so private S needs to = 0. If the person micro saves, then other entity(ies) will micro dissave so private S stays = 0.

Also it seems likely that C will fall if no entity borrows or issues stock.

Are those right? Thanks!

[edward conway]

Nick: I was not going to comment on this I=S debate and the philosophy of national income identities until you mentioned Hayek. Hayek is always an excellent palliative for too-Keynesian thinking. As for I=S: in a robinson crusoe economy, not only does I=S, but I is identical to S. Hayek tells the story (in Pure Theory of Capital) of Robinson spending all his waking hours climbing trees to gather bananas. 10 hours per day allows him to gather 10 bananas to be satisfied for the day. Obviously his income is his consumption. Robinson realizes that if he spends only 7.5 hours of his time on gather bananas and now spends 2.5 hours of his time on fashioning a stick to knock the bananas from the tree he will consequently, in future (emphasis!), be able to spend only 2.5 hours of the day on gathering the same number (10) of bananas as the stickless-gathering. Robinson will in all future periods (ignoring stick-depreciation) have 7.5hours freed up time(emphasis!).

Everyone should see perfectly easily that in this story, the "saving" of 2.5 hours of Robinson's labour-time (priced at 25% of the daily banana-gathering or 2.5 bananas) is perfectly identical to robinson's "investment". (this is a different thing from 'hoarding', which as you know, consumed the keynians and Howtrey in the interwar period)

As for the fixation on the national income identity: the day before making the stick: Y (10 bananas) = C (10 bananas);

In order to appreciate the theory of the national income identity, we have to face the fact that on the stick-making day, strictly speaking: Y(7.5 bananas) = C (7.5 bananas). we are very tempted to throw S on the right hand side of the equation. it is obvious that S=I in this case and we can logically "price" S and I at 2.5 bananas. But what does the national income identity measure? "actual" income "actually" taken from the tree on the stick-making day in question (only 7.5 bananas)? if so we omit the notional saving and investment from the right hand side of the equation.

recall that the early theorists on capital seemed to solve this problem by conceiving of "advances" (savings from past periods) which were actually paid to the stick-making robinson on the stick-making day (2.5 bananas) for his stick-making work. So under the 'advance' theory of the national income identity we would be back to Y (10 bananas) = C(7.5 bananas) + I (2.5 bananas advanced to robinson from past period savings).

ECC (Carleton MA 88)

[Henry]

"...on the stick-making day.......Y(7.5 bananas) = C (7.5 bananas). "

I would say his income on stick making day clearly was :

Y = 7.5 bananas + 1 stick.

How you would value the production of one stick for income accounting purposes in a non-monetary economy is another question.

What motivated RCs behaviour is also another question all together. He could see the possibility of producing 10 bananas in 2.5 hours leaving 7.5 hours for other activities. The value of future production for him was significantly greater than the loss of 2.5 bananas while making the stick.

[Nathan Tankus]

on the macro level saving is determined by all the output purchases that weren't consumption (that includes inventories of consumption goods). focusing on an individual's choice to save 100 dollars is misleading because we don't know if any non-final consumption output has been purchased. Incidentally Marx makes this point when he criticizes Smith for breaking down all national income into "revenue" in volume two of capital.