(Actually, tools allowing you to use money that you don’t actually possess have existed in Japan for centuries. A quick search turned up one source* saying that multiple such systems have existed since at least the Muromachi period. And now I’m interested in reading up on when and how the idea of credit first came to Japan, but… that’s beyond the scope of a kotowaza post, so we’ll leave it there for now.)
(Nai sode wa furenai; “A nonexistent sleeve doesn’t wave”)
You can’t use something that doesn’t actually exist or that isn’t available to hand. In particular, you can’t spend or give money that you don’t have. “Nothing comes from nothing.” “You can’t squeeze blood from a turnip.”
We begin three characters in, with the noun 袖 (sode), “sleeve.” This is preceded and modified by adjective ない (nai), “not,”and followed by the particle は (wa). The particle can be read both in its contrastive function (i.e. “as compared to sleeves that do exist”), and as a topic marker (“this is what I have to say about sleeves that don’t exist”). The comment on these sleeves comprises the intransitive verb 振れる (fureru), “to swing,” with negative suffix in conclusive form.
There are a number of tweaks that can be made to this one: the starting nai may be rendered with kanji as 無い; the final nai may be replaced by old-fashioned negative ぬ. The contrastive function of the は may even be made explicit by preceding this phrase with 有る袖は振れど (aru sode wa furedo, “Even though sleeves that do exist do wave, …”).
Keep in mind that this saying primarily refers to lack of money, or occasionally to a physical object that is used up, out of stock, or otherwise absent. (Before modern pockets, money was sometimes carried in a pouch secreted inside one’s sleeve.) Using it to describe a lack of something abstract, such as ideas or opinions, is generally considered an error.
*Dekle, Robert and Koichi Hamada, “On the Development of Rotating Credit Associations in Japan,” Economic Development and Cultural Change, vol. 49, no. 1, 2000, pp. 77–90. JSTOR, http://www.jstor.org/stable/10.1086/452491.
(“Gomen, Gomen! Karita okane wo kaeshitai kedo, nai sode wa furenai nda. Kinyoubi ni kyuuryou ga hairu hazu dakara, shuumatsu ni nattara kaeseru hazu.”)
[“Sorry, sorry! I want to return the money I borrowed, but you can’t pay what you don’t have. I should be getting my paycheck on Friday, so I should be able to pay you back on the weekend.”]