Hayek said that individuals make current plans for future actions based on their expectations of the future actions of others. And others might be planning to do something different from what you expect them to do. And economists need to look at what happens when those plans and expectations are not mutually consistent, and look at the processes that might make them consistent.
Keynes said that the underlying reason there was sometimes insufficient aggregate demand was because individuals who saved part of their income today, planning to buy goods with those savings in the future, did not actually place orders for those future goods today.
Hicks (I mean Value and Capital Hicks, not ISLM Hicks) said that we do not live in an Arrow-Debreu world with a complete set of markets. There are very few futures markets for goods, and hardly anyone uses them anyway. So we live in a temporary general equilibrium that changes over time partly because people's expectations change when they learn they were wrong.
Money is a medium of exchange and is what makes Say's Law wrong.
Every economist knows that, in a monetary economy, desired current expenditure on newly-produced goods is not identically equal to current income from the sale of newly-produced goods. And if they are not equal in fact, then something has to change to make them equal. Keynesians stress income as the thing that will change, others stress interest rates, or prices; but everyone agrees that something will change. Some sort of market process is needed to make them equal.
Every economist ought to be able to figure out, if they think about it for a minute, that the same is true for currently planned future desired expenditure and currently expected future income. They aren't identically equal. But do New Keynesian macroeconomists know this?
And if currently planned future desired expenditure is not equal to currently expected future income, what is it that changes currently, today, to make them equal? How would people ever figure out, today, they they aren't equal? Suppose that individuals, in aggregate, are currently planning to spend $11 billion next year. And suppose that individuals, in aggregate, are currently expecting to earn $10 billion income next year. How would they ever learn, this year, that those numbers just don't add up? If they went to the futures market this year, and placed orders for $11 billion worth of goods, to be delivered next year, they would soon find their expectations about next year's income were wrong, and would revise their expectations and plans accordingly. But people don't do this.
When we teach the simple Keynesian Cross model in first year we are very careful to distinguish desired aggregate expenditure from aggregate income. We give them different symbols, like AE and Y, just to make sure the students understand that they are not identically equal. And we draw a graph that shows they are not identically equal, and are only equal at one level of income. Then we tell our students a little story about the multiplier process to tell them what happens when AE and Y are not equal, and how both AE and Y change until they are equal. Only after we have done that do we ignore the distinction between AE and Y, and write down equations which have only Y, where Y is now understood to be equilibrium income.
New Keynesian macroeconomists are much more sloppy. They don't have two symbols, AE and Y. They just have Y. They write down an equation (actually, whole sequence of equations stretching into all future time periods) that look like this: Y(t)=Et[Y(t+1)] - F(r). Strictly speaking, that Euler equation is an equilibrium optimisation condition between an individual's current desired expenditure and currently planned future desired expenditure. It should really be written as AE(t)=Et[AE(t+1)]-F(r).
Now I'm not too worried about them failing to distinguish between Y(t) and AE(t). It's sloppy, but I know if I ever questioned them on this they would fall back on something like the same sort of story we tell in first year. If AE(t)>Y(t), then firms immediately increase output and employment to meet the extra demand, so Y(t) rises to meet AE(t). Or maybe firms raise prices, and the central bank responds by increasing the interest rate r so AE(t) falls to meet Y(t). Or a bit of both. It's a bit of a stretch to assume this process brings AE(t) and Y(t) into equality instantly, but maybe it's quick enough so it doesn't really matter if you are using quarterly data.
So it's maybe a little sloppy for New Keynesian macroeconomists to fail to distinguish between AE(t) and Y(t), but that's all it is. They at least have a story in their back pocket they can reach for if anyone questions them on this.
But it's more than sloppy if they fail to distinguish between Et[AE(t+1] and Et[Y(t+1)]. (And the same goes for (t+2) and (t+3) etc.). It's more than sloppy, because they don't have a story in their back pocket to cover their asses. And I can't think of anything that would make them equal. I can't even think of anything that would let people know they were different. We don't buy next year's groceries in today's supermarket for future delivery.
Now, if every individual knew what every other individual were planning to spend next year, and knew what every other individual were expecting to earn in income next year, and understood National Income Accounting, and could add up all the numbers, they would learn that Et[AE(t+1] and Et[Y(t+1)] weren't equal. So they would know that someone is being overly optimistic, or pessimistic, but they wouldn't know if it was them. Maybe all the other people are wrong; I'm not going to change my plans or expectations. The amount of knowledge an individual would need to figure out that he was wrong would be enough to make that individual smart enough to be appointed central planner, so we wouldn't need New Keynesian macroeconomics anyway.
There's sensible rational expectations, then there's silly rational expectations, and then there's the rational expectations that would be needed to make New Keynesian macroeconomics work.
New Keynesian macroeconomics ignores Hayek, Keynes, and Hicks. Big deal, you might say. OK, how about this: New Keynesian macroeconomics assumes that Say's Law is expected to hold at all future periods. It therefore implicitly assumes that people expect the economy to be a barter economy in all future periods. Which of course is logically inconsistent with the rest of the model, because the rest of the model has a finite future price level, measured in money.
New Keynesian macroeconomics lacks consistent microfoundations.