From an Austrian point of view, it is natural for us to get skeptical whenever we see expectation put into an economic function. For example, if we look at the Keynesian short run aggregate supply function, Y=Y+a(P-eP)+v, eP is considered the variable for expected price level, Y is considered to be the natural level for output, P is the price level, v is the variable that takes in account for shocks, and a is the amount of output that responds to the unexpected change.
Now this equation holds other non-realistic assumption like v to account for shocks, and a to account for output change due to unexpected change but for now I am just going to talk about eP.
As my Keynesian professor states, one way to derive price expectations is by using a rational view on the market, which is taking prices from all places, and current and past prices and then make an expectation. Another way to derive a price expectation is by judging the current economic environment, shocks, or conditions and then from there make an expectation.
Now it seems like the Keynesians acknowledge that there are multiple ways to derive expectations and from these different ways to derive expectations, there could be people with contradictory positions on whether their expectations have a positive or negative impact on prices. So now this begs the question: how does this function account for different expectations? And even if the Keynesians have a satisfying, which would be a miracle in itself, how can the expectations be measured in numbers? The only thing one can say about expectations in this function, assuming a satisfying answer to the first question, is that it is either positive or negative to the price in the future, so how can one derive a number from the words positive or negative?
Again, I am merely critiquing the expected price aspect of this function. There are other aspects that are wrong in this function, such as the variables v, a, it’s “natural” output, or its assumption in a single price level.