What would it take for Say's law to hold
Say thought that aggregate demand had to equal aggregate supply. This is true in the simplest model in which people trade non durable consumption goods (always called apples and oranges). Add up individual budget constraints and you get that planned spending can't be higher than planned sales unless someone made an arithmetic mistake.
John Cochrane appears to believe in Say's law. Many people have pointed out that he forgot about the existence of money. If people want to increase their money holdings then planned spending can be less than income.
It's not just about money II
Cochrane's error is not just that he forgot about money. For one thing, less liquid financial instruments invalidate Say's law too.
Cochrane has to assume that people have no wealth of any kind. Anything durable, not just money invalidates his argument.
Let's say we all plan to sell our shares (commmon stock) to buy goods and services. That way planned consumption plus taxes plus investment plus net exports can be greater than GNP. The distinction between money and other financial assets is very important in many ways, but it is not relevant to Say's law which would be invalid even if we bought and sold stock with non-durable consumption goods (apples) and not with money.
But it isn't enought to assume no financial instruments (which is odd for a finance professor but hey ...). The demand for currently produced goods can be greater (or less) than production of goods, because people can trade durable goods made long ago for currently produced goods and services.
Cochrane is right in a Walrasian model with one period or in a Walrasian model in which nothing nothing at all lasts from period to period. So a model where we trade apples for oranges is a model in which my yearly planned consumption must be roughtly equal to my yearly income. However, if the model also includes apple trees and orange trees, then this is no longer true.
If I own apple trees then my demand can be greater than my income. I have wealth (the trees). I can buy apples and oranges by selling my trees. If everyone wan't to sell trees (not made this period) to buy fruit (made this period) then planned consumption of goods produced this period will be greater than production of goods produced this period.
The value of trees does not appear in GNP unless they just matured (the value of pruning trees does). The budget constraint includes, at least, current income plus wealth (with perfect financial markets it also includes the expected present value of future labor income).
Cochrane is assuming that income = wealth. This is a much stronger assumption than that there is no money or no financial instruments.