Trade and The World's Most Misunderstood Accounting Identity: Y=C+I+G+X-M

Repeat after me:  Y=C+I+G+X-M is an accounting rule.  It does not explain anything about the economy.  It is as useful to telling us anything interesting about the economy as the equation biomass=plants+animals+bacteria tells us anything about the ecosystem.

Which is why this kind of article in the press makes me crazy (emphasis added)

The U.S. trade gap narrowed in April as the effects of a West Coast port slowdown faded, easing one of the biggest drags on economic growth during the opening months of the year....

This year’s volatile import and export figures worked out to an overall drag on the economy in the opening months of 2015....

A surge in imports and falling exports subtracted 1.9 percentage points from the headline figure. As measured by GDP, exports are a positive for economic growth, while imports are a negative...

“The huge drag on GDP from trade in Q1 will almost certainly not be repeated in Q2,” said Jim O’Sullivan, chief U.S. economist at High Frequency Economics.

Here is the logic.  The GDP is calculated by adding Consumer spending + Industrial spending + Government spending + eXports and then subtracting iMports.  Because imports are subtracted in the GDP equation, they look to the layman like they shrink the economy.  How do we grow the economy?  Why, let's reduce that number that is subtracted!  But this is wrong.  Totally wrong.   I have tried many times to explain this, but let me see if I can work by analogy.

Let's say we wanted an equation to count the amount of clothing we owned.  To make things simple, let's say we are only concerned with the total of Shirts, Pants, and Underwear.   Most of our clothes are in the closet, so we say our clothes are equal to the S+P+U we count in our closet.  But wait, we may have Loaned clothes to other people.  Those are not in our closet but should count.  So now clothes = S+P+U+L.  But we may also have borrowed clothes.  Some of those clothes we counted in the closet may be Borrowed and thus not actually ours, so we need to back these out.  Our final equation is clothes = S+P+U+L-B.  Look familiar?

Let's go further.  Let's say that we want to increase our number of clothes.  We want wardrobe growth!  Well, it looks like those borrowed clothes are a "drag" on our wardrobe size.  If we get rid of the borrowed clothes, that negative B term will get smaller and our wardrobe has to get larger, right?

Wrong.  Remember, like the GDP equation, our wardrobe size equation is just an accounting identity.  The negative B term was put in to account for the fact that some of the clothes we counted in S+P+U in the closet were not actually ours.  But if we decrease B, say by returning our friend's shirt, the S term will go down by the exact same amount.  Sure, B goes down, but so do the number of shirts we count in the closet.  So focusing on the B term gets us nowhere.

But it is actually worse than that, because focusing on reducing B makes us worse off.  If B rises, our wardrobe is no larger, but we get the use of all of those other pieces of clothing.  Our owned wardrobe may not be any larger but we get access to more choices and clothing possibilities.  When we drive B down to zero, our wardrobe is no larger and we are worse off with fewer choices.

Returning to the economy, I don't want to say that it's impossible for increases in imports to drag the economy.  For example, if oil prices rise, the imports number measured in dollars will likely rise, and the economy will likely be worse off as we have to give up buying other things to continue to buy the oil we need.  But, absent major price changes, drops in exports more likely just mirror drops in C+I+G.  If consumers are hurting, they spend less on everything, including imported goods.   At the end of the day, none of these numbers (Mr. Keynes, are you listening?) are independent variables.

Postscript:  By the way, the trade deficit is a mirage in another way - it looks at only a subset of trans-national financial transactions.   The flow of dollars is (mostly) always in balance.  So if we are net sending dollars overseas when trading hard goods, the dollars come back in foreign purchases of investments and financial goods (which aren't included in the trade numbers).  Saying we have a trade deficit is the same as saying we have a net investment surplus.  For you physical scientists out there, measuring the trade deficit is like drawing your box around the process wrong such that you miss some of the forces.

If you really want to know our trade problem, it's not the trade deficit per se, but the fact that the funds coming back via investments are largely invested in value-destroying government debt rather than productive investments.


  1. Nehemiah:

    Great post. Thanks,

  2. Richard:


    You can turn it around. How much is available for consumption?

    From Y=C+I+G+X-M you get

    C = Y-I-G-X+M

    From this you can easily see
    - government is a drag (*)
    - investment is a drag (*)
    - imports are benefits
    - exports are costs

    (*) At least for the short run

  3. What the...:

    OT/ I for one hope that in your example a change in B would have no offsetting impact on U since that would imply borrowed underwear. Ewww.

  4. NL7:

    Following the wardrobe analogy, the mercantilist presumption is that wealth is loaning out as many clothes as possible while borrowing as few as possible.

    Which has been pointed out for a long time. Bastiat made the same argument, where a Frenchman had to buy less from England for more money, so that somehow the French economy would be better off.

  5. Arthur Felter:

    Let's not forget that increasing L may seem to make our wardrobe bigger, but it does not increase the amount of clothes that we can wear.

    Also: Government comes third in the GDP equation, as does underwear in the clothing equation. I think a great correlation can be drawn here: they're all up in your junk, shitty, and need to be thrown out often.

  6. ColoComment:

    Another point to consider is that our purchases of imported goods decreased during the same period as the U.S. dollar has been strengthening (making imported goods cheaper to purchase.) We (in the U.S.) are buying less from abroad even though the "price" of everything has gone down.
    Not a good omen for the global economic outlook, I think.

  7. morgan.c.frank:

    the other great fallacy in the gdp analysis is that c, i, g, x, and m are independent variables. they are nothing of the sort.

    even in the same period, they are not independent. raise g? how? with what money? what was i? was it raw materials or intermediate goods? if you import chips and put them into a ford focus, you need the i to create c even though the car was made in the us.

    over multiple periods, they get even more interrelated, but even in just one period, if you shrink imports to zero, i'll bet gdp would plummet.

    we'd be low on energy, unable to produce most domestic goods, and the economy would trainwreck. this endless vilification of imports is absurd.

  8. a friend:

    Um, how does a port slowdown increase imports?!? We had difficulty getting our goods in.

  9. mx:

    That's the point. Imports are now up, as the port slowdown has largely ended.

  10. gr8econ:

    One of the things I try to teach my macroeconomics students is that the standard macroeconomic answer to the question, "Is that a good thing or a bad thing?" is Yes.

  11. Dan Wendlick:

    Imports are subtracted merely to keep the same goods from showing up as credits in the ledgers or two different countries, period. What the equation totally misses is that the value of the goods imported exceeds the price paid for them, or else the transaction would not have occurred.This surplus value's effect on the economy is completely lost.
    Secondly, in the nearly unique case of the US, the export of our currency is a positive good. The reserve nature of US dollars stems from the industrial, commercial, and military might both created by and creating stability, virtually guaranteeing that there will always be someone willing to exchange dollars for goods somewhere in the world.

  12. marque2:

    The flow of dollars may be in balance, but having foreigners invest with the dollars we gave them to purchase trinkets, isn't necessarily a good thing.

    Lets say I am buying an excessive amount of clothes to my kids, and then have to sell the house, and the foreigners use the money gave them to buy my house - well dollar wise that is neutral, but economically I am toast. And of course this type of exchange can't go on forever unless there is massive growth in the host county - otherwise, even the goods available for investment aren't worth investing in any longer, and we will be left owning nothing, and with no ability to purchase trinkets any longer. Our growth has been pitiful for years.

  13. herdgadfly:

    Investipedia sez:


    The systematic and comprehensive recording of financial transactions pertaining to a business. Accounting also refers to the process of summarizing, analyzing and reporting these transactions. The financial statements that summarize a large company's operations, financial position and cash flows over a particular period are a concise summary of hundreds of thousands of financial transactions it may have entered into over this period. Accounting is one of the key functions for almost any business; it may be handled by a bookkeeper and accountant at small firms or by sizable finance departments with dozens of employees at larger companies.

    What "accounting" is not is the gathering and manipulation of data to analyze the economy as a whole. Statisticians would more likely run the GDP numbers and of course that function falls under "statistics."

  14. Don:

    This is the same reasoning that some people use to decide that if you grow your own food, you'll be wealthier. As any gardener (and most farmers) will tell you, that just ain't so.

    Division of labor and specialization works, and it works across political boundaries as well.

  15. bigmaq1980:


    But, sticking with the Y=C+I+G+X-M, Liberals delight in explaining this is how cuts in government spending causes the economy to slow.

    They forget to tell anyone that the funding for government comes from the other parts of the equation.

    Also, they (with the theory) assume at least a 1:1 return on the economic expenditure in the government's hands. In fact, they talk of a "multiplier effect" (i.e. >1:1).

    Given the inefficiency of government, I've never believed that to be the case. But, it is used as an rationale / excuse for "investment" - e.g. infrastructure.

    There is much more flawed analysis/thinking behind all this, but will leave it at these key points.

  16. jimb82:

    I was just thinking that Bastiat made the same point in about 1850.

    But a much better point he made in the same essay was that a dollar of government spending, if taken from consumption or investment via taxation or borrowing, is a net zero for GDP.

    The only way to increase nominal GDP by borrowing money to increase spending is either to inflate the money supply (which would still have zero effect on real GDP) or to print money via QE (which then is lent, directly or indirectly, to finance the increased C+I+G). In the latter case, there is still a net zero effect over time because the increase in spending that is seen today is offset by a decrease in C+I+G spending in the future to pay the Fed back the principal on those bonds, which is not seen.