## Wednesday, December 21, 2016

### Why Y?

A professor emails me:
My students have the pleasure to use your economics textbook. I have one question: where the symbol "Y" for GDP comes from? All the others, we could detect, such as NX , NCO, etc. My students are curious, and I could not give them a good answer.
My unsatisfying response:
To be honest, I don't know. It is an old convention to use Y to denote real GDP, and I am just following that. But I don't know where or why the convention began.
If anyone knows the history and reason for this notation, please email me.

Update 1: Several people email me that the usage goes back to the early Keynesians, which is certainly true. Others suggest that Y is the generic dependent variable, as in y=f(x), which seems an unlikely explanation to me. Still others point out that I is already used for investment, which is true but does not explain the choice of Y for income and output. Some say Y stands for "yield," which seems a useful mnemonic, but I have never seen that word used to describe GDP in a standard published source. So I still don't have a fully satisfying answer.

Update 2: One person writes:
I thought it was well understood that 'Y' is the symbol for real GDP because it is short for "Income" as in "National Income."  Since 'I' is already used for other macroeconomic variables, we use the letter that is phonemically or orthographically related to 'I,' namely 'Y' (which is known in languages like French and Spanish as "Greek i").

Maybe this is the right answer, but one thing I am sure of is that this is not "well understood," at least not by readers of this blog, judging from the many other emails I received.

Update 3: A Harvard student looks at the history:
The earliest reference to GDP as "Y" I could find is Kalecki 1937. The first articles to formalize the IS-LM model (Hicks 1937, Harrod 1937, Meade 1937) all seem to refer to national income as "I" (for income), and Cobb Douglas (1928) calls it "P" (for production). I'd be curious to see if anyone can find an earlier reference to "Y" than Kalecki 1937. It appears there as Y=f(I) (income as a function of investment), which seems like a vote in favor of the y=f(x) argument (but I agree that's not a very satisfying explanation).
Update 4: A reader directs me to an old letter from Keynes to Hicks (dated March 31, 1937). Keynes writes:
“On one point of detail. I regret that you use the symbol I for Income. One has to choose, of course, between using it for income or investment. But after trying both, I believe it is easier to use Y for income and I for investment.”