Friday, August 09, 2013

Thinking out loud: Do government deficits equal private surpluses?

I hear a lot of people say this: "Government deficits equal private-sector surpluses," or "Government deficits equal private savings." For example, Jan Hatzius says this.

Is this true? I'm not immediately sure. It sounds true - after all, how does one save except by lending to another, and how can you lend unless the other borrows? But can I find a counterexample?

Let me think about it.

OK, first suppose there's no government. In that case, if government deficit equals private saving, then private saving must be exactly zero. That means that if total net private savings (assets) begin at 0, they must remain at zero forever.

Is that true?

Suppose that the economy consists of a number of hunters, who never interact with each other. They just hunt deer, eat some of the meat, and store the rest in the form of salted venison in their sheds out back (imagine that salted venison stays edible forever). Over the years, the stock of salted venison grows and grows.

Is it correct to say that total saving in this economy is zero? Well, it seems like the answer is "no", since households are increasing their stock of real assets. There's no debt, no money, and no firms. It seems like real aggregate saving is positive in years when the total stock of salted venison increases.

Can this be right? Do the hunters have some liabilities that I am not counting, to balance out their real assets? I can't think of any. They have no debts. They don't interact with each other at all. I could make up a corporate sector, and pretend that each household owns a "firm", but it seems like the liabilities and assets of each of those firms would exactly cancel out, leaving the private sector (households + firms) with positive total assets, due to the positive assets of households.

So it seems to me that by storing durable goods, it is possible to save by lending not to an external counterparty, but to nature itself. The private sector runs a real surplus every year, and the only deficit is nature's deficit.

Similarly, suppose we measure savings as income - consumption. Well, income (the amount of fresh venison + the amount of salted venison that enters the hunter's possession each year) is definitely more than consumption (fresh venison eaten each year) for each hunter. That seems to me to indicate that real saving is positive for each household, and thus for the private sector as a whole.

I've been talking in real terms so far. But how about nominal terms? To measure surpluses and deficits in nominal terms, we need a unit of account. So suppose that the hunters now are able to interact with each other, and to trade. Suppose that they decide that the unit of account is the pound of fresh venison. Hunters can trade salt for fresh venison, salted venison for fresh venison, etc. The amount of "money" (fresh venison) in the economy is determined randomly, by nature - i.e., some years, there are more deer to be hunted, some years less.

OK, so what about the nominal value of the real assets (salted venison) sitting in the sheds? This is determined by the nominal price of a pound of salted venison - i.e., how many pounds of fresh venison must be exchanged for a pound of salted venison. The total stock of nominal assets in the economy is given by: (lbs of salted venison) * (lbs of fresh venison / lb of salted venison)

Can this rise? It seems to me that it can. Suppose that the stock of salted venison increases, s per the previous example, but the price of salted venison stays fixed (which we can assume because we're just looking at accounting identities, not at the determinants of prices). It seems that aggregate nominal saving is positive.

So it seems to me, at first blush, that there can be net private saving without the existence of a government, and hence without net government deficits. Thus it seems to me, at first blush, that the private sector's surplus need not equal the government deficit.

But this is just "at first blush". I have only thought about this question for less than an hour, and for only about ten minutes if you don't count the time it took to write this post. Furthermore, I am not that knowledgeable about accounting conventions. So I may have missed something in this simple example. If so, please tell me what I missed, in the comment section.

Update: Some people are telling me that "private-sector surplus", as used by Hatzius and others, does not mean "private saving", but rather "private saving minus private investment". In that case, the accounting clearly makes sense, and does not conflict with my example (since storing salted venison is investment).

However, I still have some doubts about whether the true government "deficit" in this latter sense, i.e. govt. investment - govt. saving, can be measured accurately. But that's a topic for another post.


  1. Anonymous4:54 AM

    The claim about sectoral balances is purely financial, referring to (S-I) not I. In a closed economy, S-I=0 because private savings Sp = (Y-T-C) and government savings Sg = (T-G) must sum to Sp+Sg = (Y-T-C)+(T-G) = Y-C-G = I.

    Saving deer meat increases both S and I, but (obviously) does nothing to financial balances.

    1. I see. So the claim commonly stated in the press is a misnomer. When people say "surplus" they do not mean "saving", but "saving net of investment".

      This seems true.

      Of course, it also seems to me that we don't measure government's true savings correctly.

    2. Anonymous5:14 AM

      That may be true about government, depending on who "we" are. However, it doesn't really matter, here. Because it's a discussion of financial balances, the closed-economy private surplus must equal the public deficit. After all, one agent's financial asset is another's liability and all that.

      But yes, saving net of investment.

    3. Because it's a discussion of financial balances, the closed-economy private surplus must equal the public deficit. After all, one agent's financial asset is another's liability and all that.

      Right. But in any attempt to use this identity to help guide policy, you need to measure government surplus/deficit, so you can know if you're increasing it or decreasing it, and by how much. And that is hard to ascertain, because govt. investment is tough to measure (actually, so is private-sector investment, given things like human capital).

    4. Still, the ambiguity you're referring to is over what counts as investment as opposed to consumption, as in the case of human capital. Since the financial surplus nets out both investment and consumption, there's no ambiguity over the fact that a private financial surplus must equal the public fiscal deficit (plus the current account in an open economy). And regarding policy right now, the deleveraging underlying the ongoing recession is about those financial balances, not about investment as opposed to consumption. I recommend Martin Wolf on all of this.

      I'd also add a neat quote from Keynes, in reference to your example: 'the act of saving implies... a desire for “wealth” as such, that is for a potentiality of consuming an unspecified article at an unspecified time.' So salted venison is of very limited use as a savings vehicle, which, as you know, is one reason why we have financial assets.

    5. Anonymous9:47 AM

      Noah @5:31

      No, that is exactly wrong-- for exactly the reason you specified! Remember, the balances are purely financial, so they are easier to measure than investment. (Witness the latest GDP revisions incorporating IP.)

      It's I (and therefore S) which is difficult to measure, not S-I.

      However, it is true that an accounting identity is not a model. Lots of folks err in that. But it is important to recognize that if the government net financial balance improves, then that is offset elsewhere in the economy.

    6. The simpler accounting identity for me is:
      Y = C + I + G + (X – M)
      where Y is GDP (income), C is consumption spending, I is investment spending, G is government spending, X is exports and M is imports (so X – M = net exports).
      It seems, in Noah's example C is raw venison consumed and I is the amount salted. G, X & M are zero.

    7. Anonymous11:52 PM

      "one agent's financial asset is another's liability"

      What about a share in general electric? who's liability is it?

    8. I often think that it is tragic that the classic national income identity became C+I+G...., obscuring the vital government contribution to investment (notably in public infrastructure) and making it easier for right-wing commentators to dismiss government expenditure as "waste".

    9. Unanimous10:49 PM

      "What about a share in general electric? who's liability is it?"

      It is General Electric's liability because General Electric has to pay any dividends or returns of capital that may occur in the future. General Electric also has debt liabilties, and many real and financial assets, the present value of which is often uncertain due to the inability to predict the future revenue streams associated with them.

  2. Anonymous5:09 AM

    I'm not an expert, but I would say that surely the "public debt equals private surplus" makes the assumption that you're in a closed economy?

    China and Japan hold nearly $2.3trn in US Treasury bonds between them, out of $5.3trn held outside US borders. Surely that's where the majority of the surplus is?

    So yes, it's a private sector surplus of sort, but not in the US.

    1. Anonymous5:27 AM

      Yes, the financial sectoral balances in practice include the foreign balance (conventionally the current account, sign reversed.) It may also split private domestic balances into household and business.

      In the U.S., the *domestic* private surplus appears to closely mirror the public deficit and the foreign balance moves more slowly. So over the Great Recession, domestic private deficits turned into much larger surpluses so long as the government deficit grew. With the deficit shrinking, domestic private balances have begun once again to fall as a share of the economy.

  3. The deer meat currency is still a real and *consumable* product. Instead lets have a shop keeper who lends script and is willing to accept script as payment for meat, spears, or loan repayment. In period 0, Noah gets a loan of 1 script, which he uses to buy a spear. In period 1, Noah kills a deer and has 1lb of excess deer meat. Noah can a) save - by selling his deer meat to the shop keeper for 1 script, thus producing private surplus and government deficit, b) Noah can run a deficit by borrowing more from the shop to buy more spears, thus a government surplus, c) throw a big party, converting real surplus into fun, but neither government nor private sector surplus/deficit, merely the conversion of one valuable good into a different valuable service.

    Fortunately the value of both government and private assets and wealth can increase over time (through the use of capital goods like spears and labor like hunting).

  4. If you do the math the unspent income is equal S-I, not S. S is a mismomer, it is unconsumed income, not unspent income as colloquially understood. So the statement on the private surplus is purely financial, it is an accounting statement. The national accounting counts incomes and expenditures, does not mix real and nominal variables like you did.

    The private sector can accumulate beaver pelts but not net accumulate financial assets.

    1. The private sector can accumulate beaver pelts but not net accumulate financial assets.

      I'm not sure that's true. Take my "hunters and venison" example. Suppose all the hunters deposit their salted venison in one guy's shed, and the guy issues them certificates that are redeemable for pounds of salted venison. The hunters can then trade these certificates amongst themselves; the certificates are financial assets. Now, the guy who stores the salted venison certainly has a liability; he must deliver pounds of salted venison when presented with certificates. But isn't his asset a real liability, not a financial liability, since he is obligated to exchange real assets for the certificates, not financial ones?

    2. Anonymous10:01 AM

      Noah, I believe the certificates represent a financial liability. If the certificates are redeemable for "salted venison" then the shed owner may consume all the venison the hunters bring in-- assuming he is able to procure salted venision in quantities sufficient to meet the demands of those turning in their certificates.

      If you are correct, then consider the "real" balances implied by your version. The hunters accumulate venison (real savings increases). Then the hunters exchange the venision for certificates (they trade real savings for financial). But the shed owner picks up both a real asset and a real liability. So the exchange completely destroyed all net real assets! This makes no sense.

      If the shed-owner's liability being measured in salted venison is real and not financial, then so is the hunter's asset. (In which case, the venison is double-counted as an asset.)

    3. "But isn't his asset a real liability, not a financial liability, since he is obligated to exchange real assets for the certificates, not financial ones?"

      Hey, you are mixing assets and liabilities here! MMT reading required, but again, I know you want to stay confused ;)

      His *liability* is the certificate. His assets are venison. We pay off liabilities with assets. His liability (like any liability) says: "I will give up this asset upon receipt". (The asset in question may be real or financial, no matter). So the financial assets of hunters (certificates) are equal to his liability (certificates).

    4. Anonymous, that seems right. But here the distinction seems a bit semantic.

    5. Yes. The root of the word "finance" relates to final settlement, implying a bilateral contract. The venison certificates are a financial asset to the hunters and a financial liability to the shed owner, on whose balance sheet it is matched by a real asset. I therefore would not consider that an equity share should be classified as a financial asset.

  5. The simpler idea is that in terms of financial debt, for every debtor there is a saver - and vice versa. Therefore in aggregation the savings will equal the borrowing.

    People tend to think in terms of venison, seed, or whatever where you save by borrowing from your own future, but from no one else's. That's a good way to prepare for a cold winter. But that kind of 'common sense' thinking makes no sense when applied to financial saving and borrowing across parties.

    Which is why the idea that debt is bad and savings is good has been outdated for centuries. Debt is bad when the investments don't pay to service it. And savings is bad when it can't find a profitable investment. Simple, even at 4am.

  6. Let's add three simple rules to the "salted venison" story:

    1. Only mother nature can make the raw venison.

    2. We must keep an account of all raw venison harvested-from and returned-to nature.

    3. We must be able to locate any outstanding venison.

    Now we have the proper conditions for equal and opposite accounting of all venison.

    1. Let's suppose we run with this and when I hunt a deer I take a "loan" from mother nature, and presumably when I eat the meat and drop a turd in the woods I pay back the loan. I mean, this is all arm waving, so why not?

      That makes it zero sum in the long term... every dear that is hunted, eventually ends up going into the soil sooner or later (and also every dear that is not hunted goes to the same place). Guaranteed, always gives a total of zero.

      But now, I take some meat and salt the meat and hang it up in the shed. So salted meat must be worth more than fresh meat (else no one would ever make salted meat, anyhow ask your local charcuterer) which means after you subtract my liability to mother nature, my balance sheet still comes out positive.

      By salting the venison I add value, and the value-add came from me, and thus I own it.

  7. Anonymous9:12 AM

    Also, lack of growth in wages has the figure in somewhere

  8. Roger gets it, i think. A debt is a promise, so by definition involves two parties unless we are in Zen territory. If the economy is defined as composed of "government" and 'private" then, by definition any debts issued by government must be held by the private sector. This does not tell us anything useful, nor does it, of itself, tell us anything about savings (but you can add further conditions which, again, by definition require "debt" to be set against "savings"). If you add to Roger's three points two more:

    4. All trades must be made in venison or in scrip tallied against actual venison; and

    5. All trades must be settled immediately

    then the accounting conditions required will be met. Sadly none of these conditions obtain in the human world except for brief occasional moments.

  9. I am glad you asked this question. Not because I can make any contribution, but because I asked almost the same question in comments on another blog. From the deafening silence I thought I had said something so stupid that people thought it kindest to ignore it.

  10. The interesting question is: what's the optimal level of (net) government deficit?

    From an omniscient point of view, the answer is simple: it's the level that minimizes the tax rate (without requiring any future tax rate increase, or default or inflation or any other disturbances).

    But we don't know what that level is.

  11. Anonymous10:31 AM

    Financial balances (S-I) sum to zero. Savings need not. It would be odd for them ever to.


  12. Second Comment.

    We can build derivatives from the "salted venison" accounting. The hunter can pass control to those who store or consume with a stipulation that he be repaid. The record of stipulation would be "savings" to the hunter, a "debt" to the counter-party.

    The stipulation could be given to others, traded, or loaned. The stipulation could be stored in a "bank" as a "deposit".

    Are all "investments" derivatives?

  13. If they had a wise chief then in good years he could tax some of the salted venison and store it a shed and in bad years he could use the stored venison to feed his people so they could stay healthy and be able to hunt when the deer returned. But that of course is just a childish parable and has no implications for policy.

  14. Anonymous1:34 PM

    I wonder where these hunters came from and where they are going? Were they created fully formed by a deity? Are they male or female? Or do they multiply by some sort of cell division/cloning?

    This sounds like paradise to me. [just kidding]

  15. Do we count the Fed's balance sheet as private savings?

    half j/k

  16. Anonymous3:43 PM

    1. Thanks Mr. A, saved me the trouble on this.

      Noah, there is also excellent discussion at Steve Roths place between Steve Roth, Steve Waldman of Interfluidity, and Steve R himself.

      They don't solve the problem, because there are too many questions. But this series of questions are fundamental and need to be resolved.

      The stock of S = I and the flow of S = I are different too. JKH and Ramanan have been through this many times, and of course Monetary Economics by Godley starts to address this issue as well.

    2. Anonymous1:41 PM

      What on earth is the stock of S=I?

    3. Well, real accounting needs three "reports" to be complete. Cash Flows, Balance Sheet, Income Statement. You can theoretically find the third if two are defined.

      GDP or Y is a flow variable. However, there is a huge impact from the stock of S or I out there in the world. Not only that, when wading into the weeds of Noahs' questions, it gets easy to get confused between stock and flow S and I.

      It's not easy to keep it straight, as Ramanan Iver and Gunnar Mydrals point out.

      When you hear the words "balance sheet recession" It's all about the constraints associated with the stock and not flow. Monetary Policy more easily addresses flow problems, but there are gigantic problems associated with the stock of S and I. Specifically, valuation problems. There are trillions of $$ of savings out there which are infrequently valued, but still vary with changes in interest rates, and can also be loosely arbitraged through creation of new savings/investment.

    4. Anonymous1:25 PM

      I infer that by "stock of I" you mean "K" and by "stock of S" you perhaps mean net assets (A-L)?

      It's bad practice to refer to two different things by the same name. When economists refer to S and I, they refer to flows. When economists refer to K and net assets, they refer to stocks.

      Of course you'll get mixed up in your accounting if you call the capital stock "I." It's very easy to keep straight if you bother to use the names for things.

  17. Anonymous3:45 PM

  18. Anonymous4:10 PM

    If you rephrase the question as : "Does government borrowing equal private lending ?" , the answer may become more obvious.

    (Assumes closed economy , as noted above)

  19. Your update seems to be equating the words "saving" and "investing."

    Investing describes an activity that actively generates long-term returns. So, killing an animal that would provide enough meat for an extended time frame would be an investment. Building a safe storage facility for preserved meat would be an investment. Taking the time to gather salt and preserve the meat would be an investment.

    However, the non-consumed meat that has been preserved is merely a savings.

    This is really funky because we think of "investing" and "saving" in terms of money because of our environment. And I am not sure if being picky about the definitions really changes the thrust of your model.

    1. Anonymous6:51 PM


      Not consuming a newly-produced consumption good which does not fully depreciate in the current period by definition enables future consumption. Hence, we do count inventory increases as adding to investment.

      When the inventory is later consumed, it counts against investment but adds to consumption, leaving the later-period output unchanged.

    2. I agree, the investment is the means to preserve and store the meat. The meat that has been preserved is the savings.

    3. Anonymous10:08 AM

      The meat-preserving fixed capital is investment. But the preserved meat itself is investment as well.

  20. Anonymous4:39 PM

    Citizen AllenM:

    First of all, consider we are an open economy, and what do we export? Then consider our biggest export is our debt, because that is what runs the world finance and trade systems.

    So, then consider what happens when we start choking off the issuance of that debt, and start balancing our budget.

    Either we embrace the continuity of Barry Eichengreen's exorbitant privilege, or we cut off the rest of the world from our financial system and return to autarky. Like the gold standard enforced autarky before Bretton Woods.

    Meanwhile, we have morons in Congress running around with the dead ghosts of the gold standard tied around their necks (Paul Ryan and Rand Paul are the chief fools), thinking that it's return would yield a golden age. They are utter fools.

    Now, if we choke back our deficits, and slow down growth in our money supply, will the rest of the world accept a fate of becoming Southern Europe, or will they devalue first and fastest to stay alive? The Japanese struck first, and decided, well, time to allow some real domestic inflation, as 20 years of crap is enough.

    I fully expect all of the mature Asian tigers to follow over the next few years, and for people to be shocked as each one feels the pain of our tight international money (especially as we wrap up another foolish war!), and for China to be the last to accept the bitter pill of devaluation.

    If Putin was smart, he would monetize through a gold standard tie, and push money out into the economy for gold and hard resources to put a floor under his economy.

    Government borrowing equal private lending- only in simple closed models- we live in an open model with the world currency.

    And the bottom 2/3's of our own economy is running on fumes, and the pension crisis is part of it- no real returns in a shrinking economy on the domestic side.

    In short, so much is clouded by lousy viewpoints, and parochial arguments that died at the first Bretton Woods conference, yet those arguments refuse to die.

    Someday this war's gonna end...

  21. Anonymous7:41 PM

    "Suppose that they decide that the unit of account is the pound of fresh venison. Hunters can trade salt for fresh venison, salted venison for fresh venison, etc. The amount of "money" (fresh venison) in the economy is determined randomly, by nature"

    No that isn't the case. Even if they decide to call the unit of account "venison" it will be an abstract indicator of value, in much the same way that I don't require a pound of silver to be sitting somewhere in order to be able to go to the shop and spend a pound (and never have).
    This is all the more obvious with venison, since no two real pieces of venison are alike.
    The real venison, isn't money, it is just a physical commodity, or at best a representation of the money.

    Now the denizens of this village are perfectly entitled to live without money and of course, in this case the real commodities would not disappear (though it might be less efficient) and the rate at which they were exchanged might depend upon their relative abundance or scarcity - but none of this has anything to do with the existence of physical commodities invalidating an accounting method used to represent social obligations.(Which seems to be what you are trying to demonstrate.)
    If money is an abstract concept representing what we expect to receive from other members of society then of course, that which will be given must equal that which will be received.

  22. Btw, not to be mean Noah but no wonder Wall Street hires people like Hatzius (Godley's student) and McCulley (Minsky and MMT fan) who do sectoral balances and stock-flow consistent modeling while orthodox people are stuck in their DSGE swamp confused about basic accounting identities. ;)

    1. Some links for those interested:

  23. Anonymous11:53 PM

    "one agent's financial asset is another's liability"

    What about a share in general electric? who's liability is it?

    1. Anonymous12:33 AM

      GE gets your asset (the almighty dollar) and you get liability (the share can be worth no more than the book entry electrons).

    2. Anonymous1:11 AM

      So the shares I own arent actually assets but liabs instead? Im sorry I still dont understand how it is a liability.

    3. Anonymous1:47 PM

      Anon @12:33 is confused. If you purchase a share of GE stock from GE, there are two double-entries in the books.

      GE gets your dollar (+asset for GE, -asset for you)
      You get the stock certificate (+liability for GE, +asset for you)

      It's a liability to GE, because they pay dividends. Of course, they can simply cut back on the dividend per share outstanding, thereby altering the value of the stock. But you rationally-expected that. Right?

    4. To get obnoxious, unless you are buying a share specifically from GE, GE is not getting your money.

      Assets = liabilities + equity

      When you buy a share of stock or a partnership interest you are buying equity, not liability. Equity describes ownership of an entity.

    5. So from the issuers side a share may be recognised as a liability?

    6. Nathanael12:14 AM

      "So from the issuers side a share may be recognised as a liability?"

      Correct. The issuer owes future profits to the shareholders.

  24. If you look at the accounting, you get a lot of stuff carried on the books that added up gives the entity's net value. For example, if you are a profitable manufacturing firm, odds are you are carrying inventory which is worth more than its cost in terms of labor, materials and various overhead. This shows up in the balance as an increased value of assets less liabilities. The derivative shows up in the cash flow statement as the combination of materials costs, labor costs, pro-rated overhead costs, less debts incurred to finance these.

    I assume that all the Y=C+I+S+G or whatever is referring to cash flow, but there doesn't seem to be a place in macro-economics for the integrals, that is the balance sheet of assets and liabilities. Economics has always seemed to have a problem with time and state, possibly because economists have problems dealing with the relevant differential equations. Y may be equal to some alphabet sum or another, but there is no place in the equations for the changing state of the economy which is odd considering that economics is supposed to be useful for talking about economic and capital development.

    Basically, accountants wouldn't be having this discussion. The matter would seem to have been settled when double entry bookkeeping was developed in the 13th century or then about. I think one big problem with economics today is that we have forgotten that every economic argument has a corresponding accounting argument, much as every elliptical equation has a corresponding modular form. As Wiley noted when he proved Fermat's Last Theorem, when the economic argument gets bogged down, look at the corresponding accounting statement.

  25. Anonymous1:18 AM

    "the closed-economy private surplus must equal the public deficit"

    In the current system this is true. But under a system where money isnt created as debt this isnt true. For example the money supply would expand increasing private surplus while the government could maintain a balanced budget.

  26. A private sector surpluss doesnt mean the private sector is expanding at all. Private lending could be contracting by a greater amount than what is entering the system by gov deficit.

  27. Anonymous1:57 AM

    ". . . the only deficit is nature's deficit."

    Nature generates deer; the government generates dollars.

    I don't understand the difference. Isn't all you've done is change the medium of savings?

  28. If the government's "deficit" comes about by spending money it borrowed, somebody else in the "private sector" is going to have to pay it back. No net "savings" there. If it comes from squirting some new funny money upon a lucky recipient (new "net financial assets!!!!"), that lucky guy makes off for free with the goods working people had planned to buy with money earned from hard work. The price of goods goes up and working people have to raid their true savings to pay the higher prices. MMT "sector balance accounting" sure doesn't account for that. Either way, nobody has actually saved anything other than the rich purchaser of a bond who should have instead been investing in a business but for the attractive crowding out caused by the issuance of the bond. Oh, what a tangled web the MMTers weave.

    1. You failed the accounting there. Govt deficit always creates sone type of money-asset ex nihilo, be it an electronic reserve, a paper dollar, a treasury bond or a platinum coin. If then the govt swaps some of these assets promising to return the original asset to the "lender" the debt is paid back TO not BY the pricate sector.

      If you issued 2 types of autographs: pink and yellow and then borrowed the yellow one by issuing a pink one, you would pay the "debt" back TO the private sector by accepting back the pink one and issuing another yellow one. No grandchildren of anybody in the private sector are involved and there is no burden on anybody. Think of treasury bonds as pink autographs and dollars as yellow autographs - no burden in borrowing and returning them, ever.

    2. And then all you need to do is find some who will accept that platinum coin as payment.

      You can make anything add up on the books, but that's irrelevant if people just ignore your books and get on with their lives.

    3. Tel,
      I know but a sovereign government has a trick how to make its liabilities widely accepted. Invented by ancient kings, works every time as long as the state's legal and law enforcement structures exist. It is called taxes. Taxes do not pay for government spending (the gove cannot tax us a platinum coin or even dollars, before it spends them because we don't have them otherwise).

  29. Noah & everyone else:

    The model you are creating from Noah's original idea and the following discussion seems so abstracted and unrealistic that drawing useful conclusions about the real world economy from it would be almost impossible. To me it appears to be like creating and observing the a snow-globe to predict winter weather. You'll get more bad ideas from it than good except by random chance.

    One thing in particular that I'd like comment on is this statement:
    "...the only deficit is nature's deficit."

    Like ellen1910 above I don't see the hunters as separate from nature, but a part of nature. You're creating separate entities from on thing.

    In accounting terms (since this is discussion of an accounting identity) this is like saying the balance sheet section of a trial balance owes the income statement section because the balance sheet has a credit balance and the income statement has debit balance or vice versa. A lot of people seem to fall into this error of thinking.

  30. What else are they equal to then professor Smith?

    They must be equal to something... they represent something.

    Many say they are a reflection of future tax liabilities of the private sector ...... that a deficit is a tax not yet paid. The implication here is that a deficit must eventually be erased with a tax.
    So if it is a tax not yet paid then I believe that is the same as a positive dollar balance in the private sector account. It may be less positive in the future when the tax is paid but at the time of measurement it is exactly equal to the amount of money not yet paid in taxes..... which can be called a surplus.

    When the govt is in surplus they have extra tax money when the private sector is in surplus the govt is in tax deficit.

    I think Mr Hatzius is exactly right

  31. Government deficits equal private-sector surpluses

    Probably true as an accounting identity at a point in time but it ignores the dynamic effects. The interesting economics is all in the second order expansion around the first order accounting identity.

    1. You can expand to the 100th order and accounting still holds.

    2. You can expand to the 100th order and accounting still holds.

      Sure - but quantities on both sides of the "equals" sign change over time in interesting non-linear ways - hence my reference to dynamic effects.

    3. This comment has been removed by the author.

    4. Absalon, you have just described finance. And finance is basically the application of abstract math to core accounting principles in order to create transforms that describe the immediate value of a long term situation.

    5. What do you mean it ignores the dynamic effects? The whole point of the statement is to point out, especially to those who want to try and scare people that deficits are bad , is that the govts deficit is the non govts surplus. What one does with the surplus is up for discussion about whether or not its good or bad. Money is amoral, what you do with it matters. Labeling deficits as bad is simply wrong. Surpluses can be bad in certain situations but I would never say "surpluses are bad". The level of financial discussion is hopefully getting past the silly deficit and debt mania that assumes that deficits are bad and govt debt beyond some arbitrary number of 90% lead to doom. It starts with understanding what exactly "the deficit" measures. And it has nothing to do with venison or rocks. Those analogies lead to no enlightenment at all

    6. Greg - I agree with you about deficits. The accounting identity is the foundation of a conservative argument that deficit financed stimulus cannot work because it must necessarily divert resources from the private sector through borrowing from the public sector.

      The accounting identity must be true at each point in time. What I mean by dynamic effects is that deficit spending can change income and private sector surpluses over time. It seems to me that borrowing one dollar from the private sector does become one dollar less that the private sector spends on something (an alternate investment?) and if you want that dollar shifted from the private to the public sector to have a positive effect then you are going to need to look to second order effects.

  32. No offence intended Noah, but I am surprised that you were apparently not sufficiently familiar with the S=I identity not to ask such a basic question, when in other posts you seem in command of what I would consider to be hard technical modelling issues. I think it may say something about the detachment of academic economics from the everyday questions.

    1. +1 It seems Noah's experience of graduate economics is similar to mine - a clear detachment from what many would regard as the 'realities' of economic life an economist should understand.

      My 2c would be the Noah's time would have been better spend reading the technical notes to the national accounts rather than writing a blog, if he is indeed curious about what these economists mean. Maybe that's what he has since done. I know when I read these technical documents I learnt far more about how to properly infer meaning from them than I did in a whole economics degree.

      One point no one has mentioned is that the cured venison in this Robinson Crusoe-type story would actually be classified as inventory.

      The important take-away here is that there is no such thing as saving (as Noah want to think of it i.e. delayed consumption) at a macro-economic level.

      Which actually bring up far more issues that 'well-trained' economists ignore - like pre-saving for retirement and more. I describe this in more detail here.

    2. There is no S=I identity.

      Salted meat hanging in the shed is saving (you can eat it later) but not investment (it does not represent infrastructure, it does not make other work easier).

      Gold coins stacked in a box are a saving, but not investment.

    3. Anonymous7:01 PM

      Tel, changes in inventories should and do count toward investment. An increase in inventories *obviously* enables future consumption.

  33. I also find it odd that in trying to answer a question about the degree to which a measurement of a govts financial position is simply a reflection of an opposite position in the non govt, your first response is to assume away the govt! How is it helpful to assume away that which you are trying to understand?

  34. Nathanael12:12 AM

    The true accounting identity is a lot more subtle than this.

    Private saving minus private investment == TOTAL CHANGE IN MONEY SUPPLY.

    Not all money is government-produced, which is why it isn't quite true to say this:

    Increase in Money Supply == Government saving minus government investment.

    It's pretty close to true, but the problem is (as usual) banks. We faced a massive reduction in the bank-manufactured money supply in 2008.

    (I'm being sloppy here. This only works over a short time period. Over longer time periods, you get into tricky stuff like velocity of money.)

    1. Nathanael12:13 AM

      There is no way to meaningfully measure savings by banks and other financial intermediaries, and apart from incidentals (such as the branch buildings) they don't do investment, which means that analyzing them requires some extra work.

    2. Nathanael12:17 AM

      Bleh, I was being sloppy.

      DECREASE in Money Supply == Government saving minus government investment

    3. I don't get why people forget about the change in money supply in this equation. It clearly must be true, and very important, but left out of descriptions of "accounting identities".

      The another problem here is that nobody seems to want to give much attention to dimensional analysis. (However, wikipedia seems ahead of the curve here,

      This is why many people get confused between what's often called "stocks and flows" and then get themselves in huge tangles trying to argue for dimensionally wrong equations. There are other problems such as quoting debt/gdp as a percentage (which is wrong) and having additional terms in these accounting equations which don't have the same dimensions as all the other terms.

  35. Anonymous1:04 PM

    I don't know why but discussions like this remind me of the Hebrew Bible discussion of rivers running full the the sea but the sea never fills up.

  36. I hear a lot of people say this: "Government deficits equal private-sector surpluses," or "Government deficits equal private savings." For example, Jan Hatzius says this.

    It's not true. This is (or should be) obvious. Moreover, the two quotes are not even equivalent. The first relates to _surplus_ saving, suggesting that private saving necessarily exceeds private investment by the value of the government's deficit, which is wrong as a universal proposition. The second equates private saving with government deficits, which is simply and straightforwardly wrong.

    What _is_ true is the following:

    1, In a closed economy, the government can make the difference between nominal saving and nominal investment arbitrarily large or small;

    2, In a closed economy, the difference between the real value of private saving net of private investment is the real value of government borrowing.

    1. Anonymous7:32 PM

      The government is utterly incapable of creating a wedge between saving and investment in a closed economy. Utterly and completely.

      Any financial asset must as a matter of accounting be a financial liability for someone else. So in a closed economy, net financial assets are zero. That leaves saving in the form of non-financial assets. That is, investment.

    2. In a closed economy, net assets at the national level are zero by definition. Net assets for sectors *within* that economy are not zero by definition, however. In particular, net asset acquisition by the private sector equals government borrowing.

    3. Anonymous1:02 PM

      I am not sure I follow you. Where do you mean private and where you mean economy-wide?

      Let us split government expenditures into G (government consumption) and Ig (government investment) For clarity, we will call private investment Ip

      Sp = Y-T-C and Sg = T-G, but government borrowing is (G+Ig)-T = Ig-Sg. Thus,

      Sp-Ip = (Y-C-Ip)-T = (C+I+G-C-Ip)-T = (Ig+G)-T = Ig-Sg = "government borrowing"

      Hence, your (2). But rearranging terms, we get


      That is, saving is exactly equal to investment. So if (2) is true, then (1) must be false.

  37. Some other views here (Roche & Carney in the comments):

  38. Noah,
    there is a difference between the real economy and the financial economy. The accounting is talking about FINANCIAL assets (i.e. the debts of others). Real assets are another category - which may or may not be used as collateral for financial assets.

  39. Anonymous12:13 PM

    It may have already been said, but it seems to me that the model you outlined makes the real value of the salted venison stockpile equal to zero. If I understand the model correctly, the hunters can always hunt more fresh venison than they can eat. Additionally, the hunters appear to prefer fresh vension. If the hunters can always and anywhere, hunt more deer than they can eat, there is no reason to stockpile the salted venison. It will never be eaten, because the hunters will always just get more fresh venison. If true, this means that private saving does equal zero.