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.
Worthwhile Canadian Initiative 
Nick,
I don’t understand why interest rates don’t change in your model. After the shock, everyone tries to save more, because of the part of the shock they believe is idiosyncratic and they are consumption smoothers. Interest rates MUST therefore adjust, because there is a market clearing condition where savings and consumption must come from total production.
Also: You say the central bank cannot react quickly. I don’t understand what a central bank is doing in this model, as there’s no money.
Andy: it would normally make sense for the interest rate to rise when there’s a (positive) aggregate shock. But if the agents observed the interest rate rise, they would know there must be an aggregate shock, and that would solve their signal extraction problem. So I would need to complicate the model by adding one more shock, so they still couldn’t distinguish aggregate from individual producer shocks. So I assumed the central bank sets the interest rate using some sort of Taylor Rule, but has a one period lag, so can’t adjust it to smooth out aggregate demand
I think you are implicitly assuming aggregate production is constant, and does not respond to aggregate demand. I am assuming a monetary economy with temporarily sticky nominal prices, and imperfect competition, so an aggregate demand shock will cause aggregate production to increase temporarily, if the central bank doesn’t raise interest rates immediately. All this is standard NK macro.
By the way, you and Adam are forcing me to clarify my thoughts. Always good (for me).
OK. I’ll admit… I took up defending Nick’s argument without actually having read any NK papers. Ever. I was just defending the logic, but knew nothing of the premises – sorry Nick. So now I want to read some, and I started with the Eggertsson and Woodford referenced above. On page 149 we get the following whopper: “For simplicity we assume complete financial markets and no limit on borrowing against future income.” OK, I get it. If we can hedge out our idiosyncratic risk, then we all become representative agents. So now we can all form our expectations under the modelers measure. So in this case Nick is right – the model assumes complete markets => single agent rat-ex => coherent expectations for income and expenditure.
The way I see it, any model that assumes rational agents in a complete market, implies model-consistent, single representative agent expectations. It also succumbs in general to Nick’s criticism, not only in its reduced equilibrium form. [It also assumes I’m going to keep working after I’ve hedged all my future income in the complete market. Whatever.]
This is an entertaining piece about DSGE in general: http://blogs.ft.com/maverecon/2009/03/the-unfortunate-uselessness-of-most-state-of-the-art-academic-monetary-economics/. It fails, however, to mention the problem of income stream hedging.
This time with a link that works.
@K, It is simply not the case that rational agents in a complete market imply single representative agents. There is a great deal of work on this topic. Look up the Cambridge Capital Controversy or the Mantel-Debreu-Sonneschein Theorem for more on aggregation results. Franklin Fisher has a nice book called “Aggregation” as well. I will say further that if you have a coherent proof that complete markets with rational agents imply a single representative agent, you can easily get that published in a top Econ journal. That is a Nobel level result, if mostly because people believe it is not true.
More broadly, pointing out that models have certain unrealistic assumptions is neither a novel nor a particularly point. Yes, everyone knows that, including the people who wrote them. The question is whether we can still learn something about economic mechanisms with simplified models. The answer is obviously yes. In fact, you do something similar every time you make any economic argument.
@Nick, I am definitely not assuming that production is constant. You seem to want to peg prices (ie interest rates) but then you must allow another margin of adjustment such as the level of production. The market must respond to the change in savings demand. You cannot shut down all adjustment mechanisms and then complain that there is no current period adjustment that would inform consumers of what’s happening.
Nick, I don’t really think you’re understanding your own example here. This is not progress.
In your example the positive (transitory) aggregate shock leads to higher consumption today and agents expect higher consumption tomorrow then they’re actaully going to get.
There will be other negative (transitory) aggregate shocks that lead agents to lower consumption today and to expect lower consumption tomorrow then they’re actually going to get.
On average their conditional expectations are correct (the expected value of the conditional expected value is the right number). That is all that rat-ex requires, rational expectations means the expectations are rational. It does not mean that expectations are correct with probability 1.
If agents expect higher consumption tomorrow which leads them to consume more today how is any thing in the NK model wrong? If tomorrow arrives and that expectation turns out to be wrong (which it usually will since new shocks will arrive) what goes wrong? Nothing.
New shocks arrive each period, just because we tend towards a steady state does not mean we spend all our time in it. (We actually spend virtually no time exactly in steady state).
Just to clarify my last comment:
In the reduced form IS equation you would still have the (constant) value of E[Y(t+1)]. It’s just that none of the agents individually expects his consumption to fall back.
The result here is of course that the real interest rate has fallen. Tomorrow when everyone learns that the shock was not permanent for anyone then it rises back. The CB doesn’t do anything to make all this happen.
Furthermore, Andy is quite correct that Nick has implicitly assumed that agents can’t observe the real rate. Otherwise they’d all be able to deduce today that the shock was transitory. But if there’s no money or bonds then that’s a valid assumption (and the real rate is a shadow real rate, it can’t cause anything since intertemporal substitution is not actually possible).
But Nick, you’re not assuming a monetary economy. If there is a real rate then it would have fallen (remember, everyone saved half their extra endowment as well). This would then reveal to everyone the shock was aggregate and thus transitory.
Adam:
I am assuming a monetary economy.
I am explicitly assuming the interest rate is set by the central bank and does not change for one period (because the central bank is slow, or has a 1 period information lag), so that agents cannot tell if the shock is aggregate and transitory or individual and permanent.
“In your example the positive (transitory) aggregate shock leads to higher consumption today and agents expect higher consumption tomorrow then they’re actaully going to get.” Yep.
“There will be other negative (transitory) aggregate shocks that lead agents to lower consumption today and to expect lower consumption tomorrow then they’re actually going to get.” Yep.
“On average their conditional expectations are correct (the expected value of the conditional expected value is the right number).” Yep.
” That is all that rat-ex requires,…” Well, no, rat-ex requires more than that, because it’s more than saying that the unconditional expectation of the subjective expectation of X equals the unconditional expectation of X. But let that pass, because it wasn’t what you meant.
“It does not mean that expectations are correct with probability 1.” Yep.
“If agents expect higher consumption tomorrow which leads them to consume more today how is any thing in the NK model wrong? If tomorrow arrives and that expectation turns out to be wrong (which it usually will since new shocks will arrive) what goes wrong? Nothing.” Yep. There’s nothing wrong there. This is what’s wrong:
“In the reduced form IS equation you would still have the (constant) value of E[Y(t+1)]. It’s just that none of the agents individually expects his consumption to fall back.”
Suppose a positive aggregate shock hits. The modeler knows this, the agents in the model don’t. If none of the individual agents expects his future consumption to fall back to the unconditional average level of consumption (100), you can’t put 100 in for expected future consumption in the Euler equation IS curve. The modeler knows that the average agent will have consumption of 100 next period, and all agents knows that the average agent will have consumption of 100 next period, but the average agent believes, rationally, given his limited information, which is less than the modeler’s, that he will consume 105 next period. Each agent thinks he is above average. Just like in the Lucas 72 model, where each agent thinks his price is above average, when there’s a positive aggregate shock.
Just to be explicit, agents’ behaviour is based on their subjective beliefs, which will be different from the modeler’s beliefs even under RE if the agents have less information than the modeler. Consumption today depends on the agents’ beliefs about next year, not the modeler’s. What belongs in the consumption-Euler equation are the agents’ beliefs, not the modeler’s.
And if you want to drop the assumption about the 1 period lag in the central bank’s response, just add a random noise term into the Taylor rule. When an agent sees demand for his haircuts increase, and the interest rate rise, he doesn’t know if it’s in response to an aggregate shock, or if it’s just noise (a mistake by the central bank). So he thinks there’s still a chance that it’s a producer-specific permanent shock. This means that the interest rate would need to have a bigger average response to aggregate shocks to stabilise aggregate output than if agents could observe aggregate shocks. And a mis-specified Euler equation that used the modeler’s expectation rather than subjective expectations would underestimate the parameter on the aggregate shock in the optimal Taylor rule.
Andy: K didn’t say that complete markets are sufficient to model aggregate behaviour using a representative agent. K said that complete markets are sufficient to model expectations using a representative agent. They all expect the same thing, even if their preferences don’t allow aggregation. And that’s germane to this post, because I am talking about aggregating expectations. I know we can’t really aggregate over preferences, and the NKs know this too, but we all cross our fingers and do it.
Andy: “@Nick, I am definitely not assuming that production is constant. You seem to want to peg prices (ie interest rates) but then you must allow another margin of adjustment such as the level of production. The market must respond to the change in savings demand. You cannot shut down all adjustment mechanisms and then complain that there is no current period adjustment that would inform consumers of what’s happening.”
OK. I need also to assume that agents either don’t observe aggregate output contemporaneously, or else there’s some other shock or noise that prevents them inferring an aggregate demand shock from that noisy signal.
” If none of the individual agents expects his future consumption to fall back to the unconditional average level of consumption (100), you can’t put 100 in for expected future consumption in the Euler equation”.
Yes, that’s what I keep saying. At least you finally agree.
” Each agent thinks he is above average. Just like in the Lucas 72 model, where each agent thinks his price is above average, when there’s a positive aggregate shock.”.
Yes, so? How is does this make the model inconsistent again?
“Just to be explicit, agents’ behaviour is based on their subjective beliefs, which will be different from the modeler’s beliefs even under RE if the agents have less information than the modeler. Consumption today depends on the agents’ beliefs about next year, not the modeler’s. What belongs in the consumption-Euler equation are the agents’ beliefs, not the modeler’s.”
Again, yes, that’s what I keep saying.
And then you solve the model…
So which part of what you’re saying here implies that:
“New Keynesian macroeconomics lacks consistent microfoundations”?
Nick, here’s the part I think you’re missing.
Before we’ve solved the model then everyone has 5$ more consumption in today’s consumption and 5$ more in tomorrow’s. But their income was $10 today so they also have $5 of savings. These savings hit the bond market and lower yields.
Now, you have in mind that the CB is pegging the nominal rate so it responds by tightening, lowering the money supply. Let’s suppose that prices and velocity are completely fixed, then this lowers income back to it’s steady state value.
If you want to say that the CB doesn’t react at all because of you’re one period lag assumption on it then the nominal rate falls, revealing to all agents that the shock was aggregate and thus transitory. Knowing the truth agents respond accordingly.
(There are other possibilities as well…)
In both cases (with emphasis, not worked up), AFTER WE SOLVE THE MODEL, it is all consistent and and agent expectations have been brought into line with the reality of the equilibrium.
@Nick: You’re correct, I misread K’s passage. Apologies, K. However, I do not understand what “model-consistent, single representative agent expectations” means. Individual agents can have rational expectations, or some other expectations. Where is the link to a representative agent?
I do not believe that ratex models require all agents to have the same expectations. For instance, in the model Nick described, each agent has a slightly different expectation on what aggregate productivity will look like in the future because they are each solving a different signal extraction problem based on the combination of their idiosyncratic shock with the aggregate shock. What’s important is that the agents know (a) the distribution of possible idiosyncratic and aggregate shocks, (b) how all agents and the markets will respond to different realizations of these shocks, and (c) how these responses map into the information an agent himself can see (ie, the signal extraction problem is solved correctly).
Nick, I don’t see how inventory changes show a difference between planned spending and planned output. It seems to me they show a difference between actual spending and planned output.
I’m skeptical about whether any differences that exist are important in macroeconomic terms. I believe recessions are caused by tight money, and I can’t imagine that tight money policies would be correlated with systematic differences between planned expenditure and planned output. After all, consumers and producers have access to the same macro data.
Kevin, Thanks for reminding me not to use the Krugman/Wells text.
I guess we’ve gone in circles enough here but there is an important point here.
First of all, to the extent Nick even has a point it is a critique of ratex, not NK models.
If anything he should be praising NK models for their robustness to relaxing the ratex assumption, as Evans showed.
The other point here is that Andy is right, ratex doesn’t require everyone to have the same expectations, especially with incomplete information. Complete markets does give everyone full information because prices reveal it but again, if you don’t like that assumption you still don’t have a valid criticism of NK models since again, NK models don’t in any way need that assumption.
So again, why isn’t Nick praising the robustness of the NK paradigm?
Finally, I suspect some of the confusion on this discussion is that Nick sometimes seems to be treating equilibrium to mean steady state equilibrium where then everyone does expect the same things. But you can be in equilibrium out of steady-state, Nick’s Lucas 72 type example is a shock that knocks us out of steady state. Besides the example having nothing at all to do with NK models it does not show a problem with the approach in general.
Finally though, I think it does matter in the sense that you have, for example, Richard Serlin come and ask Nick, ‘so basically NK models have no basis in reality because of crazy unrealistic assumptions…’ (clearly a paraphrase) and Nick say ‘yep’. It’s not true but how can general blog readers tell the difference? (Richard himself should really know better but evidently not). Most people will take the authority of the proffessor blogging over the anonymous, first name only, commenters even though the professor is not neccessarily right here. I see the same dynamic repeated on other, perhaps more widely read blogs, and I get genuinely scared. How’s the general public ever going to know whether those in authority are doing the right thing?
As a PS: And Andy was spot on when he said how you really need the math. Much of the circles we ran with Nick were in focusing on different sets of equilibrium conditions at different points in the debate because it’s hard to keep track of them all in a verbal discussion. But of course you do need them all. Futhermore, though verbally we tell causal type stories the reduced form system of equations that the equilibrium of the economy is the solution to doesn’t say anything about causation. Everything is jointly determined (once in reduced form), nothing is causing anything else. This seemed to me to be another point of confusion.
Of course, perhaps I’m wrong and Nick is right but would all these people, from Evans to Woodford really not of noticed this point? It surely isn’t that subtle.
Scott, if mikeb (September 13, 2010 at 01:56 PM) is correct you’d better beware of Mankiw too.
My summing up:
There’s a difference between aggregate planned future consumption and expected future aggregate consumption. The former belongs in the Euler equation, not the latter. They are only equal, and only equal to the model-builder’s expectation of future aggregate consumption, under very stringent conditions, not just rational expectations. You need common knowledge of all contemporaneous information among all agents.
I actually like rational expectations. I do not like rational expectations plus common knowledge of a lot of information that agents won’t in fact have and can’t be expected to learn.
When the typical NK model just bungs Et[Y(t+1)] into the Euler equation, all these problems get swept under the rug. This will result in errors. Now all models are false, but in this case I think it will lead to systemic errors in the model. For example, if individual shocks are more persistent than aggregate shocks (because, for example, the central bank can stabilise aggregate shocks but can’t stabilise individual shocks), the errors in the mis-specified model will be systemic, not just random.
I both like and dislike NK. I am an NK, in some respects. But I think there’s things wrong with current NK. This is an internal critique.
I like both words and math. Math helps clarify words; words help clarify math.
“Equilibrium” means “whatever the (simultaneous) model predicts”. It doesn’t always mean “long run equilibrium”. But it’s always worth asking about the process that gets us to equilibrium. That’s stability, in the broader sense. If we weren’t in equilibrium, would agents have the information to revise their plans and beliefs in a direction towards equilibrium?
Must prepare for class.
PPS: and it is a bit annoying I guess how Nick responds to comments but ignores what they actually say, better to not respond (less going in circles).
What I mean is:
Here’s Nick again: “There’s a difference between aggregate planned future consumption and expected future aggregate consumption. The former belongs in the Euler equation, not the latter.”
and “When the typical NK model just bungs Et[Y(t+1)] into the Euler equation,”
Seriously, how many times in the comments was it pointed out that no NK model “just bungs Et[Y(t+1)] into the Euler equation”, that the models in fact put indiviual planned future consumption in the Euler equation and not expected future aggregate consumption?
How many times was it pointed out that the reduced form, where Et[Y(t+1)] appears, is not a behavioural equation but part of a model that has already been solved and had equilibrium imposed? The only sloppiness is that we do still refer the resulting equation as an Euler equation but that’s because it’s supposed to be clear to anyone who understands the model and how it was derived.
I think those Hicks (Hickses?) are the same person, John Richard Hicks. I appologize if you did that intentionally to highlight changes in style.