A picky, cranky, wonky blog post. Nice cloudy, cool afternoon, though.

I had leave time to burn up at the end of the year, so I’m still home and at my leisure on the Monday after Christmas, looking out my window at a beautiful drizzly gray day   So it’s curious and a little discordant that I’m slightly bugged about something.  And it bugs me that I’m bugged.  And what’s more, it bugs me that being bugged about this bugs me.

I’ve just read a Center on Budget and Policy Priorities report by Dean Baker, part of a more general CBPP discussion on full employment, in which I encountered a use of accounting that I think is just wrong, and for which I’ve chastised others.  To be clear, I agree with almost everything in the Baker paper; I almost always like Dean Baker’s posts and papers.  He’s one of the economists I go to when I find myself adrift and want a quick whack of reality.  And this paper is saying some very basic, very true stuff.  I agree with his premise, which is that the level of employment and the wage rate for workers in the United States would both improve if we could reduce or eliminate our trade deficit.  I agree with his primary conclusions, which are first, that the most direct and best way to do that is to reduce the value of the dollar against the currencies of our trading partners, and second that this is going to be politically difficult to do because there are a lot of vested interests against it.  And I agree even with his secondary conclusion, which is that the most obvious way to counter a large trade-deficit depressant is with a large budget-deficit stimulus.  

But along the way he uses accounting identities in a way that I think is misguided, and that seems to me to imply a misunderstanding of the word “identity”.   I know I have to be wrong about this, because almost every economist alive and most of the smartest economists in history seem to do the same thing that Baker does in this paper.  But the process he uses seems dangerous to me; if it’s accepted it seems to me as though we can prove a lot of things that are completely false, and that can lead us to harmful policy choices.  And for the life of me, I can’t figure out why I’m wrong, and why what he does is reasonable.  Please, if you know where my mistake is, write a comment.  

Here’s what he does that crosses my eyes. (I’m going to write these things so they look like algebra, but what they are really is just columns of figures that are summed---there’s nothing abstract or mysterious here, and nothing terribly mathematical.  This is accounting, not fluid dynamics.)  He lays out the usual absolutely elementary macro equations, starting with the first and foremost, which is precisely table 1 (or more specifically, table 1.1.5) from the National Income and Product Accounts:

(English translation: total national income, Y, is the sum of income from the sale of consumer goods C, the sale of investment goods I, sale of goods and services to the government G, and net export sales, meaning exports minus imports.  In the NIPAs those are all the recognized sources of income---and the result of this sum is generally reported as GDP.)

So far so good.  I like that part.  It’s unassailable.  In fact it should be written like this:

 Which makes it clear that this isn’t an accidental equality, not an equilibrium point that we’re trying to achieve: Y, national income, is defined to be the sum of the incomes received from all sources.  We measure all the variables on the right, and then we calculate Y by adding them up.  I want to emphasize this, because somehow everyone appears to lose sight of this about identities.  These accounts are tables; Y is the thing that appears at the bottom where you write “total”.   (The NIPA table puts it at the top just to confuse everyone.)  So no matter what the values on the right side of this equation do, the equation is always true, because Y is always just the sum of all the other variables.  If all the other variables magically double in an instant, the only result in the accounts is that Y doubles too.  

Having said that, I should hasten to add that there might be real world constraints that make it impossible for all the other variables to double at once; we have limited resources, limited existing plant and equipment, a limited population of workers.  But the constraints are in the world, not in the fact that this is an accounting identity.

Then Baker offers the other half of the equation we all saw the first day of macro-econ class:

Which actually doesn’t directly show up in quite that simplified form anywhere in the NIPAs.  It’s there, but is pretty spread out through the other tables.  I leave the equality sign as it is because this isn’t the definition of income.  It is the definition of something else, but I’ll come to that in a moment.

Then he rearranges these two equations this way:

This follows by simple algebra from the equations above, and it gathers the accounts into groupings that we read about all the time in the news.   The first term in parentheses is the trade surplus, and the last term in parentheses is the government budget surplus; both of these have been significantly negative in recent years, so they’re usually called deficits---the trade deficit and the budget deficit.  But my eyes are already beginning to cross, because it seems to me that this form already implies a bit of misdirection.  Because with this as a basis he tries to show that the X-M term, the trade deficit, somehow pushes around the T-G term, the budget deficit.  Here’s how he starts: 

“Let’s imagine for a moment that…all of the private sector’s savings is devoted to private sector investments.”

Now, why would we imagine such a thing?  More later on this, because this particular imagined equality is a very common motif in economics, and one with a long history, but let’s follow the logic here first.  Clearly he wants to say that the term (S-I) is zero, or at least fixed, so any change in (X-M) must be matched by an identical change in (T-G) in order to maintain this “identity”.  Voila!  The trade deficit creates a corresponding government budget deficit.  

The trouble with this argument is that we don’t get to specify what is fixed and what is not in this accounting equation.  At least not due to the accounting.  Because the second equation up there, the other half of the basic-macro-class lesson, should be written something like this:

and substituting for Y in this, we can restate Baker’s equation above like this:

But the accounts only specify that S will change when the other variables change, not that the other variables must bear any specific relationship to each other.  Because savings is just whatever is left over after all expenditures are taken out of current income.   It’s what you would put at the bottom of the column of figures and call something like “net income” or “residual income”.  The NIPA accounts don’t see it as something we do, or a decision we make, it’s just the final result, the difference.   As far as I can recall without actually looking it up, there are only two kinds of things the NIPAs just define from their internal arithmetic: totals like Y, or residuals like S.  In fact all the totals are some variation of Y (GDP, GNP, NDP, NNP, etc), and all the residuals are some variety of S (corporate retained earnings, household savings, government surplus, etc.)

(A quick aside---notice that in the equation above, income is represented by I, G and X---income from selling investment goods, selling goods and services to the government, and selling goods and services abroad---and the subtractions are only T, taxes, and M, expenditures to sellers outside the country.  Why aren’t other expenditures included?  Because my expenditure is your income: every purchase from a domestic supplier subtracts that income from the purchaser’s account, but adds it to the seller’s account.  Total national savings doesn’t change.)

To be fair, I’m certain that Baker knows all of this very well; better than I do, I’m sure, since he gets to do this stuff all the time, and I can usually only do it in the evenings after work.  He knows that he needs some additional arguments outside the accounts to justify any relationship he asserts between the variables, and he’s careful later to specify that the trade-off between government deficit and trade deficit is implied only if we want to maintain full employment.  But the accounting sleight of hand is there, whether he really believes in it or not, even if he’s just using it as a way to introduce his topic. 

My point is that the belief that the trade and budget deficits are linked may be true, but it can’t be drawn as a conclusion from the accounting equation alone.  This may sound picky, but it matters; if we accept this logical process of using the accounting identity as a forcing economic function as valid then it would be possible to create a claim, from the accounting identity, that any one of the variables is “forcing” a change in any other.  Just fix everything else by assumption, and danged if the variables you have in mind aren’t the only ones that change! For example, let’s go with Baker’s assumption that S-I is fixed, or at least very sticky, and then assume that we’ve passed a balanced budget amendment so that the government deficit is always zero.  Then we have proved, from the accounting identity---haven’t we?---that any change in exports must always and instantly be matched by an exactly equal change in imports, and in the same direction.  If exports increase, then imports, by this logic, would also increase by an identical amount.  How on earth would that happen?  In any short run, I don’t have any idea.  It pretty much violates the usual views of how exports and imports change in the short run; they generally change in opposite directions due to a change in exchange rates.  But if we were allowed to fix everything else in the accounting identity above, it would have to be true.

I said above that this process of thought is dangerous.  Here’s why.  This kind of argument is very familiar; it’s exactly the kind of argument that makes people claim that budget deficits “crowd out” investment due to this same accounting identity.  To make that argument, you would rearrange the terms like this:

Then the “crowding-out” crowd would say, “Let’s imagine that the trade deficit (X-M) is fixed and savings S is fixed---then an increase in the budget deficit (G-T) must come out of investment!  Where else could it come from?  Those are the only two things we are allowing to change.  If all the other variables are fixed, how else can the equality, the identity, be maintained?”

But as I explained above, within the accounting we don’t get to decide what variables are fixed.  If we declare that any are fixed, or that there are relationships among them we have to add behavioral equations or other forces outside the accounting framework to explain those things.  The crowding out argument doesn’t get to say that S is fixed, unless they can show some reason that it should be: as we saw above, within the accounts S is whatever it needs to be to balance the equations; it is just the difference between income and outflow.

And what’s unfortunate in this case is that everything Baker needed to make his argument is in the first equation right at the top.  We have to add a “full employment” level of Y to get there, like this:

Where Y-hat is a fixed goal, full employment income, and to get Y to equality with Y-hat, the other variables have to be prodded into line.  If the trade deficit (X-M) gets “bigger” (more negative, but bigger in absolute value), then one or more of the variables on the right must be made to grow, not because the accounting says so, but in order to satisfy our desire to achieve the fixed Y-hat goal. This is straightforward demand management, which is where Baker was really going.  It’s where he did go, in fact.  But he could have stated that at the outset, and then proceeded to discuss how we could make the other variables cooperate with our goal.  There are alternatives.  For example: we could simply have the government spend more (increase G directly), but we have to take into account what that increase in income from a low Y might do to consumption or investment---as a matter of behavioral response, both of those might depend on total level of income.  Or we could decrease taxes, and depending on how we do that our action might increase investment, or consumption, or both.  

Or we could do what Baker is suggesting: try to lower the value of the dollar, so that we export more and import less, and the increase in net exports helps to push our domestic income toward full employment....

The comment on S=I that I promised will wait until another post.  It’s time to take a walk in the cool afternoon, and start thinking about what to make for dinner.