My colleague who shall remain nameless (he is smarter than me … OK, that eliminates … none of them) and I were talking about the silliness of national income accounting today. In particular, we were talking about a NY Times article that claims for every dollar of US government spending, we would get an additional $1.50 of total output!

Sounds like the ultimate free lunch … why doesn’t the government just take every single dollar that is out there right now (as if it is all hanging off a tree) and spend it all themself? That would mean that our current $14 trillion would turn into $21 trillion! And then simply rinse and repeat, and whala … we get $31.5 trillion … before you know it, we’ll all be infinitely rich. Sadly, this sort of rubbish passes for good economics in the year 2008. Maybe it is because it is the season of Santa Claus?

In any case, to see why such “multiplier” effects are nonsensical (ignoring for now the 800 pound gorilla that is called “opportunity costs’), let’s write down a simple national income identity that ignores investment and international trade. Without loss of generality we can express national income (Y) as the sum of household consumption (C) and government spending (G):

Y = C + G

If we believe that consumers spend 75% of their additional income, then C can be rewritten as 0.75Y. Substituting into the equation above we get:

Y = 0.75Y + G

And with some simple algebra you will find that:

Y = 4G

Every dollar of government spending results in $4 of increased income! The Keynesian free-lunch.

To see why this is nonsense, let’s just write down another identity that has to be true:

Y = Y(Wintercow) + Y(Everybody else)

If the total income in this economy is $10 trillion, and Wintercow’s income is $50,000, then we know that:

Y(Everybody else) = 0.999999995 x Y

And substituting this into the above, and doing a little algebra, you get:

Y = 200,000,000 x Y(Wintercow)

So, according to the same identity, every dollar spent by Wintercow would generate **$200 million** of additional income! The ultimate free lunch, no?

Pop quiz time … what is wrong then, with the national income accounts and the Keynesian multiplier?

I’m glad that I’m not the only one who thought those models were complete rubbish. On one example with a model of that sort, I found at least three significant math errors, including setting two terms as equal then changing one of the terms without the other because it’s assumed to be constant (how can you set it equal,then?). I’ve determined that you should never use a model of accounting (Y=C+I+G+NX) for a model of growth (Y=f(L,K…)). They ignore too many things like monetary effects and opportunity costs.