Consumption booms and austerity

There is a bit of maths in this post. Don't worry, it is really very easy - otherwise I wouldn't be doing it. (You all know about me and maths....)

Dean Baker has just produced this post pointing out that the existence of the US's trade deficit has implications for private sector saving levels. The point he is making is that it is not possible to have an increasing trade deficit while cutting the public sector deficit unless the private sector is prepared to spend more. Unfortunately this doesn't come across too clearly in his post, and it was misunderstood by people who read his post when I retweeted it on Twitter. Here's an example:
No, that isn't what Baker meant. Let me explain.

Baker is implicitly using the sectoral balance equation, which in its simplest form is this:

Private sector (savings - investment) = Government (spending-tax income) + External (exports-imports)

I'm bored with writing out words, so here it is in algebra:

(S - I) = (G-T) + (X-M)                         (1)

I like to note how S is derived because I find it unhelpful to ignore consumption spending. S in this equation is the excess of private sector income over consumption spending:

S = Ypriv - C                                         (2)

I shall use this later on. But rearranging the first equation to reach Baker's equivalence of national savings with the external balance gives us this:

(S - I) - (G-T) = (X-M)                          (3)

I'm just going to put the words back in this for the benefit of those who like me find it difficult to remember what algebraic terms mean:

Private sector net savings - government net spending = external balance         (4)

If I set the external balance to zero, thus eliminating it from the equation, we can see then that:

Private sector net savings = government net spending.                                    (5)

In other words, when external trade is balanced, for the private sector to be able to save government must run a deficit. If government wants to run a balanced budget, then either the external balance must also be in surplus (i.e. a trade surplus) or the private sector must reduce savings.

But the US has a trade deficit (M > X). So the amount on the right-hand side of equation (3) is negative. What does this imply for the left-hand side?

Equation (3) suggest that if the external balance is negative, then net government spending must be larger than private sector net savings. This could take the form of government profligacy sucking in imports, of course (Greece, maybe). But that's not the only possible explanation. Suppose that government were running a balanced budget (G=T). That would set the second term in equation (3) to zero, giving us this:

S - I = X - M                 (6)

So when government runs a balanced budget, private sector savings come entirely from exports. Therefore, if M > X, then S - I (and therefore by extension, Ypriv - C - I) must be negative. There can be no private sector net savings when government is running a balanced budget - or, heaven help us, a primary surplus - and there is a trade deficit. The desire of the fiscal authorities to keep their own house in order forces the private sector to spend more than it saves, funding the difference either by drawing down existing savings or by taking on debt.

Fortunately for US citizens, the US has a fiscal deficit (G > T). The US private sector has been deleveraging sharply (which is the same as running a positive net savings balance) since the financial crisis, so a substantial fiscal deficit has been both necessary and unavoidable, and so far the government has made little attempt to interfere with it.  But there is a worldwide crusade for governments to cut their deficits, and the US is no exception. Baker's point is that if the government reduces its fiscal deficit then either the trade deficit must reduce or the private sector must reduce its net savings level (i.e. stop paying off debt and start spending). And as he rightly says, is this what we really want? Surely it would be better to allow the private sector to maintain its savings level so it can reduce its awful debts to something more manageable and maybe store up something for the future? Is the fiscal situation really so desperate that a damaged private sector must be forced to take on more debt and/or cut back spending even further than it already has, so that the fiscal balance can improve? Which is more urgent - private sector healing or fiscal repair?

Where Baker causes confusion in my view is in his suggestion that the trade deficit would be unaffected if there were an austerity program aimed at cutting the fiscal deficit, and that there would therefore be a consumption boom. I don't believe it. A damaged and indebted private sector is not going to go into another consumption boom any time soon. Nor is that the experience of other countries. The evidence from the Eurozone shows trade balances in distressed countries improving dramatically, not because exports have increased (though to be fair in some cases they have) but because of drastic cuts in imports. But trade deficits aren't the only things that reduce when governments embark on austerity programs. Countries that have tried to cut their fiscal deficits while the private sector is deleveraging have caused the private sector to cut spending further in order to maintain savings levels, resulting in economic contraction. That's essentially what the IMF admitted in its recent "mea culpa" about fiscal multipliers. Fiscal consolidation after a major financial crisis hurts the private sector far more than had previously been thought.

It also isn't true that in the 2000s the private sector consumption boom was in any way related to public sector austerity. This was a very confusing suggestion on Baker's part, and I don't think he meant it to be interpreted in that way. In the 2000s both private and public sectors were net spending: Ypriv < (C + I) and G > T. A government austerity program at this stage wouldn't have made any difference to the private sector's consumption, because of the easy availability of cheap credit. But it would have reduced the trade deficit. 

Which brings me to my final point about the US's trade and fiscal deficits. The US dollar is the world reserve currency, and US debt is in demand worldwide as the primary "safe asset". The worldwide demand for both far exceeds the needs of the US economy. Until this changes, the US must continue to run substantial trade and fiscal deficits, because otherwise the financial system will grind to a halt. A government austerity program aimed at reducing debt issuance would reduce the worldwide supply of safe assets still further, giving further impetus to the search for a replacement for US Treasuries as the primary safe asset - and by implication therefore also the US dollar as the reserve currency. If the "right-minded people" Baker castigates actually succeeded in their "holy jihad" to reduce the US's fiscal deficit, they could push the world into an even worse financial crisis than the last one. They should be careful what they ask for.

Update: In the comments to this post, Ramanan pointed out something that I had missed. Baker claims that if there is a trade deficit, the national savings position of the US must be negative. This is true for savings net of investment (S - I), but it is not true for savings themselves (S).  To say that the US cannot have positive national savings if there is a trade deficit is not correct. It may indeed have positive savings - but it might not have much in the way of domestic investment.

Update 2: Cullen Roche has also pointed out the decomposition of S into Investment (I) and savings in the form of net financial assets (S - I). I'm still reading about the implications of this, but I'm posting Cullen's link here.

Update 3: As this post assumes people are familiar with the basic national accounting identities, I've added some notes on these as a link at the end (kindly provided by @occidens on Twitter).

Related links:

Dean Baker, CEPR             Has anyone heard of the US trade deficit?
Blanchard & Leigh, IMF     Growth Forecasts and Fiscal Multipliers (pdf)
Sober Look                        Eurozone crisis has eliminated periphery trade deficit
Coppola Comment              The illogicality of the IMF
                                           When governments become banks
Wikipedia                           Triffin dilemma
Christiano                           Notes on national accounting and balance of payments


  1. You are right.

    First Baker himself makes a mistake about accounting identities. He confuses saving with "saving net of investment".

    It is possible for all sectors to have positive saving even if the economy is running a deficit on the current account.

    Second, he is also inaccurate about behaviour.

    A fiscal contraction reduces national income and hence imports and leads to an improvement of the trade balance. Perhaps a big enough contraction even leads to a surplus.

    Of course this is not a way of running the economy. But Baker presents things as a "no-go theorem".

    1. Ramanan, I can't see how it is possible for all sectors to have positive NET saving if there is a current account deficit. It is possible for EITHER the private sector OR the public sector to have positive net savings - but not both.

      A large enough fiscal contraction can indeed lead to a trade surplus unless it clobbers national production so much that exports collapse as well. You say it is not a way of running the economy - but that is exactly what is going on in the Eurozone periphery.

    2. Frances,

      I did not mean NET saving (as is saving net of investment) but just saving.


      Saving of all domestic sectors = Investment - CAD

      If investment is greater than the deficit in the current account of balance of payments, the right hand is positive and we have positive saving.

      Good or bad is different but purely as a matter of accounting what he says ("if we have a trade deficit then by definition the United States as a whole has a negative saving rate.") is wrong.

    3. Let me reinterpret this in the terms I used in the post. You seem to be saying that:

      (S-C) + (T-G) = I + (X-M)

      That isn't possible. You've reversed the direction of government expenditure. I showed above that where trade is balanced, Government savings (T > G) are only possible if private sector savings are negative (S < (I+C)). That's because Government can only run a surplus by extracting money from the private sector in the form of taxation. Government savings require private sector DIS-saving. Therefore you can't have a situation where there is a trade deficit but both domestic private sector and public sector are saving. One or the other must be in deficit. If you think otherwise, please explain the maths?

    4. Frances,

      There is no C in the first identity you wrote.

      The full identity includes all current transactions with the rest of the world but let's go with yours.

      S_priv + (T - G)= I + X - M

      In the simplest case assume not investment expenditure by the government. So T - G is the surplus of the government and also its saving.


      S_priv + S_gov = I + (X -M)

      Now, X-M can be negative but I + (X-M) can still be positive.

      Hence S_priv + S_gov can be positive even if X-M is negative. Not in all cases but the statement is about possibility.

    5. Yes, you can take C out. It makes no difference - all it does is change the definition of S. I was taking the view that all income is savings until it is spent, and investment and consumption are both components of spending. And it is helpful to see that if S reduces it can impact I and C differently depending on the preferences of the private sector at the time. However, the more common form of this equation leaves out C. Whatever.

      I think the problem is that Baker is using misleading terms. He clearly means net savings, i.e. the excess of income over consumption AND investment. And that was how I interpreted his statement. It is not possible for net savings to be positive if there is a trade deficit and government has a primary balance. But I agree it could be possible for gross savings to be positive.

      From an accounting perspective both are correct. It all hangs on the definition of S.

    6. Hi Ramanan,

      Further to my last.....

      For the avoidance of confusion I've changed the post to make the definition of S clearer. I haven't removed C, just used it differently.

      I haven't added your point about Baker's misleading use of the term savings. However, with your permission I would like to add that as an update at the end.

    7. Yes sure you can add that.

  2. You might be interested in Sydenham's empirical Law which undermines the sectoral equation.

    1. No, it doesn't undermine it. If the government is running a deficit, spending exceeds tax income. Your post incorrectly assumes that increases in public spending necessarily cause taxation to rise. They don't.

      There is a huge problem with the direction of causation here, too. If you look at the US public spending vs GDP chart (first chart in your post), you will see public spending heading upwards to balance the deep recession of 2009/10. We know that that increase in public spending was CAUSED by the collapse of private sector GDP - it was public sector bailouts and operation of automatic stabilisers as unemployment rose and real incomes fell. It would be reasonable to assume that other spikes in public spending at times of private sector collapse were similarly a response to the problem rather than the cause of it - but you have assumed the opposite. Please explain why?

      The New Deal spending did not choke off a recovery. What choked off the recovery was the premature fiscal tightening of 1936. If you look carefully on the last chart in your post you will see that public sector expenditure fell in 1936 and the double dip recession followed in 1937. The deep recession in the early 1930s is the one point in that chart where public spending did NOT increase to compensate for the private sector collapse. Not surprisingly, it remains in American folk lore as the Great Depression.

    2. The reason Sydenham's Law is called a "Law" is that in the past 60 years rising public spending always accompanies falling private sector growth in the UK and US economies.

      The graphs in the article Sydenhams Law of Public Expenditure and Economic Growth are all empirical data. They contain no assumptions.

      The analysis of Sydenham's Law is, as you point out, problematical. Does rising public spending cause falling private sector part of GDP or is it, as you say, a reflex response? If we look at the 1930s the data show that private sector GDP growth was recovering before the New Deal expenditure. It is only as public spending is ramped up that private sector GDP growth falters. Similarly, in the UK data we see a rise in public sector spending in 2005 that was ideological, not due to global economic conditions or faltering GDP growth, and private sector GDP falls "pari passu". The other inflections in public spending in the 30s have the expected effect on the private sector, rises cause falls and vice versa. It is only with the mega spend of the war years that truly huge public spending raises the private sector briefly.

      In the UK Data (Graph 2) there is an entirely ideological increase in public spending in 2005 and it is immediately accompanied by a fall in private sector growth.

      The other factor that puzzles me is that increased private sector growth would be exploited by UK socialist governments to increase public spending but in every case the rate of public spending increase decreases....

      PS: thanks for discussing this. I am truly puzzled by this empirical data that appears to contradict orthodox views.

    3. You are still assuming that correlation=causation, and in one particular direction which (I assume) suits your ideological stance. You can't assume that two concurrent peaks on a chart are necessarily related, and nor can you assume that one necessarily causes the other. There are other factors - for example, interest rates were progressively hiked from mid-2004 onwards, which would have caused a slowdown in private sector growth starting from 2005. What is more surprising is that private sector growth appears to have recovered immediately prior to the crash despite higher interest rates.

      I've also now checked your data set for the 1930s (at the end of your post), and I suggest you re-plot your graph on a simple linear basis. Graph 1 in the Sydenham post is a second derivative - it plots the RATE OF CHANGE of GDP growth, not GDP growth itself. Therefore when the line slopes downwards it simply indicates that growth has slowed, not that it has reversed. To say that a temporary slowdown in the rate of positive growth indicates that public spending is choking off recovery is simply wrong. The figures show that the private sector grew throughout the period 1933-38, despite the New Deal spending.

      Non-public sector GDP is as follows:

      1929 91.92
      1930 79.28
      1931 64.33
      1932 46.26
      1933 43.78
      1934 53.19
      1935 58.52
      1936 67.04
      1937 74.68
      1938 68.42
      1939 73.15
      1940 80.98

      Actually you have the same problem with your UK data graph. It is a second derivative. I would be a bit careful with what you deduce from it if I were you.

    4. "To say that a temporary slowdown in the rate of positive growth indicates that public spending is choking off recovery is simply wrong. "

      True. Public sector spending increases appear to be reducing the rate of recovery. They appear to be slowing recovery down. But we need to know more.

      What is clear is that recovery was well underway before the large increase in public spending of the New Deal, private sector growth being positive just before the New Deal spending, and that as public spending increased the rate of private sector growth decreased. Did the New Deal inhibit this growth? We need to know why the second derivatives are so tightly coupled. The tight coupling of the second derivatives is fascinating because, since 1950, it has the nature of an inevitable and fixed relationship.

    5. I don't think you can make any assumptions about the direction of causation without knowing far more about what else was going on at the time. Yes, Chart 4 does appear to show a growth slowdown between 1933 and 1934. But after that growth picks up again and the curve actually follows the public spending growth curve with a slight lag - which suggests that if anything private sector growth was supported by the New Deal public spending, not choked off by it. You have homed in on two points to support your argument and ignored what the rest of the curve suggests.

      The causes of the 1938 contraction have been clearly identified as premature tightening of monetary and fiscal policy. I'll send you the academic papers on this if you wish.

      You haven't considered the possibility that the rises in public spending are caused by the public sector compensating for loss of private sector investment in economic downturns. That is consistent with the sectoral balances equation: if I reduces, then assuming that S and (X - M) remain constant, (G - T) must increase - i.e. the public sector must run a deficit. I've already discussed the possibility that I is forced to reduce BECAUSE OF increasing (G - T), but that can't possibly be the case when output is falling. Under these circumstances it is more likely that (G - T) would increase to compensate for a fall in I. It seems likely to me therefore that both crowding out and crowding in effects are present in your curve, and you don't have enough information to determine which is operating when.

    6. The essential feature of the relationship between changes in public spending and changes in private sector growth is that it is empirical. The data are not assuming anything.

      The big problem is explaining the data. The data are so consistent over the past 60 years that they have the nature of a "law". But, as you say, what causes what? Thanks for all of this "food for thought", I will think about your last paragraph in depth.

  3. Saving and investment are equal. Always

    1. True, but not at a sectoral level. Only at the global level.

    2. Is there proof that savings and investment are always equal? What mechanisms ensure this is so?

    3. "Saving and investment are equal. Always"

      Additionally to Ramanan I would add that saving is always defined ex post whereas investment is mostly ex ante. This differences introduces crucial behavioral elements which define the much bigger macro picture.

    4. This codifies the central fallacy of this entire discussion.

      Savings do not equal investment because incomes do not equal expenditure. Savings may remain uninvested.

    5. If you look at the equation again you will see that under most circumstances S must be > I. Which means that there will always be a proportion of savings that are not invested. Cullen Roche's link explains this by decomposing S into I, which is direct investment in the economy, and (S - I), which are net financial assets (cash and government debt). The accounting identity derived from that is:


      Hence the (S - I) in the main equation is not the whole of S, but only the part of S that is "uninvested" as you put it.

      In other words, the government deficit and trade deficit together account for the proportion of savings NOT invested directly in productive activity within the domestic economy. It follows that when the government deficit and trade deficits are large, S > I by quite a bit.

  4. The UK is breaking up: did you get the memo?

    The Economically Out-of-Date Nation-State

    1. Good article, considering this is a spam comment (as it has nothing to do with the post!)

  5. Well, it does, you see: the trade deficit + austerity is squeezing out the fat into the private sphere so that a self sustaining agricultural boom can begin to take place in the US, and various other areas no doubt, based on:

    1) the need to feed the world
    2) the lack of farmers
    3) the median age of farmers (too old)
    4) freedom & liberty

    1. You're thinking that agriculture could be the solution to the US's trade deficit? Do you think the US COULD "feed the world"?

    2. Quite so. You will learn just as much if you consider DoubleLine's recent conference call for a second: Another famed US financier looking for a slightly similar angle is Jim Rogers, though he seems to be betting more on Asia. I personally favour America because it is able to act (and react) more quickly thanks to its unique type of flexibility (governance is essentially already privatised).

      Also, although the US has problems with conflicts of interest - as each State on Earth does - to me at least, it is less opaque than China. But, then again, maybe that's only because I do not speak their language.

      I have also just uploaded the slides for your convenience, Frances:

      Perhaps it would be best, however, if you first acquainted yourself with this article:

      I have tried to show you why I think that about US agriculture. Hope I have remained on topic enough for you.

      Best Wishes

    3. I should have added, sorry, the state of play as far as we are concerned is as follows:

      Imagine a man (US economy) who's jumped out of a plane, and is now speeding towards the Earth. When Gold is let loose it's like the sudden halt of a parachute, causing Stocks to plummet, but not in dollar terms ;-) So at around $15,000 for Gold people will buy the dip for stock in agriculture, helping to generate a fairly remarkable return to mother nature, if you will.

    4. Okay, I've got you now....Freegold, yes?

    5. For one country to produce all the food for the world would turn the rest into slaves - or beggars.

    6. have to remember, with me, there's 0 point in talking about any "country"; a 'geographically contiguous state' is an alien idea, a fiction, no matter what you call said state, seeing as any and all states can only ever be one person or a group, who by definition move around. BUT ANYWAY, no I do not think that only one (relatively) small group of people is going to "produce all the food for the world".
      And no, I have no idea about freegold. Just the State-money-franchise is ending, clearly! If it helps, imagine X person produces food for Z and Z produces clothing for X.

    7. Would you please identify yourself. It's hard talking to someone who is faceless and nameless. I accept anonymous posts because some people find Blogger's sign-in protocol difficult, but I would prefer it if serious posters identified themselves.

      You are entitled to your views on the nation state, money, production and so forth, but I can't see what they have to do with a post that is discussing how funds flow around nation state economies.

  6. Government is in a state of anarchy, so order is now slowly emerging from the shadows:

    1. I would like to take this opportunity to remind you of my comments policy.

      1) Please confine your remarks to the subject of the post

      2) Please be polite and refrain from personal attacks on me or on other commentors.

      I am very happy to publish comments in the interests of constructive debate. But this blogsite is not the place to grandstand your own agenda that has nothing to do with the subject of the post.

  7. This equation is misleading: (S - I) = (G-T) + (X-M).

    The problem lies in the fact that there are two meanings of the word “save”. There is, first, “accumulate cash”. And second there is “sacrifice current consumption so as to build up an asset with a life of more than say 3 years and anything up to about 100 years.”

    The equation is true in the saving (or “dissaving”) cash sense. However it is certainly not true in the “build up assets” sense. Think about it: suppose the dividing line between consumption expenditure and investment expenditure is the above 3 years. And suppose there is a shift from spending on stuff designed to last 2-3 years to stuff designed to last 3-10 years. That implies that G,T,X or M have to change, which of course is nonsense.

    It’s the above ambiguity that leads to Anonymous above saying above that “Saving and investment are equal. Always.”, and to the subsequent comments.

    I suggest those using the equation always make it clear they are using it in the “saving or dissaving cash” sense.

    1. Ralph,

      I defined S in the post:

      "S in this equation is the excess of private sector income over consumption spending"

      Since income and spending are both flows, S must also be a flow, not a stock. Asset buildup - accumulated savings over time - is a stock.

      This equation describes flows, not stocks. Therefore it applies to the current period only, not to savings over time. It is entirely correct to state that within any given period, global savings and investment flows are equal, unless we are trading with Martians. But that doesn't mean that sectoral ones are.

      I thought you were an MMT fan? This is the standard MMT sectoral balances equation. Cullen's link explains the decomposition of (S -I) to include net financial assets separately from investment, thus resolving the tension between the Keynesian equivalence S = I (except in distressed circumstances) and the requirement of this equation that S > I.

  8. Are there ONLY two meanings to the word “save” ? Surely each person thinks differently, no? I mean, there can be a rough, generally agreed upon idea, but definitions are by definition not entirely fixed

    1. When using equations we do have to have agreed definitions. In the post, I gave the usual definition of savings in this equation:


      Can I please refer you to my reply to Ralph above regarding the difference between savings as a flow and savings as a stock. This is the flow definition, because the equation is a flow equation.

      The word "save" itself has many different meanings, but only one of those meanings can apply in each use of the word.

    2. Wouldn’t it be best to say something like (NS) = (G-T) + (X-M), where NS is “net saving of cash by the private sector”?

      I’m not happy with the following definition given by Frances: "S in this equation is the excess of private sector income over consumption spending". Reason is that that drags in concepts like the difference between consumption spending and spending which is of a capital investment nature. The latter difference is irrelevant to the “cash movement between sectors” question.

      Does that improve things?

    3. Ralph,

      I think you've misunderstood the equation. It is flow of funds, not cash movements - they aren't the same thing. Capital investment is included in the equation as I in the identity (S - I). By defining savings too narrowly as "cash" you force exclusion of non-cash forms of savings acquired in that period - which (along with cash) make up "net financial assets" in JKH's expansion of S to S = I + (S - I). I really recommend you read Cullen's link.

      Keynes' definition of savings is this:

      Savings = excess of disposable income over consumption spending

      That's pretty much the definition I have used and the definition required by this equation.

  9. "Using equations" without regard for practical reality caused a global depression, by the way.

    1. But we are using these equations with reference to practical reality.

    2. Some would disagree:

      The Tiny Dot

  10. What's the mathematical equation for waste, fraud, abuse, crony capitalism, money printing, changes in accounting rules which has led to flat wage and wealth growth for the bottom 90% as the top 1% has captured 90% of these gains over the last 40 years?

  11. When we're releasing Gold prices for food will increase because the central bankers have been playing up, but the market can solve this issue:


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