Why Does Y Equal Real GDP?

I hesitate to post this while Nick Rowe is on vacation, because he’s always so generous with his replies and explanations. Here’s hoping he gets back to this.

But he does get me thinking. I’ve spent several days re-reading and pondering his Identity Economics post and (his) related others, which post begins [my brackets]:

Here are two macroeconomic identities:

1. Y=C+I+G+NX [the National Income Identity]

2. MV=PY [the Identity of Exchange]

Both are true by definition.

Without (for the moment) burdening you with all my thinking, here’s the question that I’m left with:

By convention and practice — “by definition” — Y in these identities equals real GDP. Y means ”real GDP”.

Here’s why that doesn’t make sense to me:

Say that in Year 1, U.S. GDP (IOW, Y) is $14 trillion. That’s the total dollars spent on real-world, newly-produced goods and services. This quantity is necessarily counted in dollars, because that’s how the measurement is done (at least in the expenditure approach) — adding up all the dollar-denominated purchases/sales.

Assume: in Year 2, the economy produces that same quantity of real goods and services, and their aggregate human utility is unchanged. Real output is unchanged.

But in Year 2, the prices are 10% higher (for whatever reasons). Measured, counted GDP (a.k.a. “Y,” total dollar transactions) increases by 10%.

If Y is real GDP, then real GDP just went up by 10%. Even though real output didn’t.

This doesn’t make any sense to me. Shouldn’t Y mean nominal GDP?

Even: mustn’t it? Because it’s always counted in nominal dollars.

This would give us:

MV = Y


Y/P = Real GDP

This seems much more tractable and conceptually coherent to me. The “real” definition keeps running me into (what seem like) conceptual/arithmetic contradictions.

I was going to stop here, hoping to keep this discussion focused, but as I’m about to post I find that Saturos has given me a very nice response to my comment over at Nick’s place. The confusion expressed here fully explains the more profound confusion in that earlier comment; I simply assumed therein, based on the fundamental construction of the National Income Identity (and the methods of national accounting), that Y means nominal GDP.

Saturos sez:

Talk to any Keynesian and you’ll find that they’re far more inclined to interpret Y = C + I + G + NX as referring to real (CPI or GDP deflator adjusted) quantities. Of course P is here assumed to equal 1, because “prices don’t matter in the short run”. But I agree that it makes far more sense, and is far more consistent with the Keynesian approach, to talk about nominal spending flows. (Really, you should use lowercase for real variables, and uppercase for nominal – and the identity is true in either case, as it’s just a listing of the different categories that any spending or output must fall into.) Matt Yglesias (http://www.slate.com/blogs/moneybox/2012/05/13/fun_with_accounting_identities.html) has a new post in which he takes Scott Sumner’s version: MV = C + I + G + NX. That might be the best approach of all – it shows you that all the changes in “income accounting” variables that get reported on the news must all be manifestations of fluctuations in the overall volume of spending, MV. If we’re talking about fiscal policy or “exogenous shocks” to NGDP, then this must be a fluctuation in V (base velocity).

My responses:

1. Are you telling me that economists don’t even agree on what Y means? Not sure if that’s what you’re saying. If so, doesn’t Nick’s “by definition” start this whole discussion (even: the whole discipline of national-accounting-based and monetary economics) on a bed of quicksand?

2. Is it really standard practice to “use lowercase for real variables, and uppercase for nominal”? Seems like a great convention. Do economists adhere to this convention consistently? They don’t seem to. (If Y equals real GDP, shouldn’t it always be lowercase?) Nick uses uppercase throughout in his post, except here in his #3:

If I re-wrote the first identity in nominal terms, as PY=PC+PI+PG+PNX, it might invite the same question. Or if I re-wrote the second identity in real terms, as Y=Vm (where m is the real money stock), I could hide that question.

I presume that m = M/P. So Y = VM/P. This says rather explicitly that Y is real GDP. (So it should be lowercase, no?) So, also: is Nick a Keynesian? Sometimes, sort of…

3. Mediocre philosophical minds obviously think alike. Matthew’s (and Scott’s) MV = C + I + G + NX is exactly where I went in my first stab at this post, which I’ve discarded or at least put aside for the moment.

4. I’ve been coming to the same conclusions about NGDP and velocity. Cf. the subtitle to this post.

I’m going to add one last thought here, to thoroughly muddle the waters: Somebody could presumably argue that price can’t increase by 10% unless the utility derived from produced goods — real output — also increases by 10%. That would resolve the apparent contradiction inherent in the Y = real GDP definition. (At least as that contradiction seems to arise in my example above re: the National Account Identity.) But I can’t really conceive a very convincing empirical and/or theoretical basis for that assertion.

Cross-posted at Asymptosis.