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 
Could you elaborate on how the Euler equation is an equilibrium condition? I’m pretty sure it’s just an optimization condition. You can substitute feasibility conditions into it, but it still follows from optimization, and not from pricing adjustments. That is, it should hold for individuals (or the representative agent) even if prices are such that the economy is not in equilibrium.
Nick, You said:
“When we teach the simple Keynesian Cross model in first year”
Are there any textbooks that still have this model? I don’t recall it being in Mankiw’s text (which I use).
Also, is there any data suggesting that at some points in time aggregate planned expenditure differs from aggregate planned income? If so, what is that data, and where would I look for it? (Assume I don’t buy the Keynesian theoretical model, but do buy the New Keynesian model.)
I think you are right about the connection between Say’s law and the market for money, and have always regarded that as a key difference between old and new Keynesianism.
“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.”
So is Say’s law defined as “desired current expenditure on newly-produced goods is equal to current income from the sale of newly-produced goods”? is it just assuming that all sales have fufilled desired demand? I know the moniker “supply creates demand” gets thrown around but the way Say’s law is used is somewhat muddled since Austrian economists (Including what Say wrote in his) use it in a completely different manner. The Say’s law that I am familiar is along the lines of that one must produce a good before they can demand the goods of others. I’m not sure if it really matters for your analysis of new Keynesian economics but I’d be interested in hearing a little more of your thoughts on Say’s law.
Nick,
“New Keynesian macroeconomics lacks consistent microfoundations.”
But they solve constrained maximization problems to get those equilibrium conditions.
Nick,
BTW, that last comment was sarcastic.
Pooh Pooh,
You are fiddling Nicholas. Now you are pissed off with the NKs because they will not just capitulate to an intuitive ho hum just so story but rather have the tenacity to suggest an equally oblique story. Come one what is the fresh water micro story here that is so shall we say incontrovertible?
Scott: Even expectations that are linked by an observable, executable static arbitrage can fall apart. (eg corporate bond basis arb profits could be locked in at as much as 20% of notional over the past two years). If you want to claim that two expectations should be the same despite the fact that they are not even observable (never mind arbitrageable) then the onus ought to be on you to prove it – not on Nick to diprove it.
While we wait for Adam P… Would the budget constraint bring everyone into line?
Nick, a few things.
First, this: “It should really be written as AE(t)=Et[AE(t+1)]-F(r).” No, really it should be C(t)=Et[C(t+1)]-F(r). In the canonical model we can replace C with Y because the canonical model there is not capital and thus C=Y. But the equation is a linearization of a utility maximization condition, you get utility from consumption not expenditure.
Which brings me to the main point, at the individual level there is absolutely no reason that expected expenditure should be equal to expected income. The fact that we have a nominal interest rate means that nominal debt contracts exist in principle, each individual can plan to borrow or save. Thus Et[AE(t+1] need not equal Et[Y(t+1)].
Of course, at the date, since no capital means aggregate savings must be zero something will adjust. If the interest rate or prices don’t adjust then income will, but I don’t see any logical inconsistency here. If the interest rate doesn’t adjust properly then we can get inflation or recession/disinflation, just like in real life.
Should economics help maximize satisfied needs or maximize profit?
Nick
How would I be wrong if I added a couple of things that make it worse?
– something like a third of production and consumption is not traded, and people shift activities between the market and non-market sectors. So I can sell something for money I have not bought with money, and vice versa. So there is no reason to expect that money will have an equilibrium.
– “money” covers a lot of things, not all of equal or certain value, and changing relative to one another as well as to goods and services. So I can trade poor money for good (or vice versa), using information asymmetries or off-market resources such as social or political power/prestige. So no reason to expect money and goods to be in equilibrium either.
The analogy in my mind is that money is a simple language – and just as words in a language do not have fixed referents, but depend on their contexts for meaning, money has no single referent. Some aspects of Hayek come close, but he seems to have thought a “perfect” language was possible, when in reality it is not.
“Money is a medium of exchange and is what makes Say’s Law wrong.”
In a freshwater model with money, in the form of a cash-in-advance constraint or something like that, doesn’t Say’s Law hold in some form? I thought Lucas wrote out some models like that, though I haven’t studied them. That suggests the problem for Say lies elsewhere. But perhaps you intend ‘money’ as shorthand for the impracticality of barter, incomplete markets, uncertainty etc. There’s lots of things that can make Say’s Law wrong.
“Are there any textbooks that still have this model?”
Krugman-Wells covers it in Chapter 11: Income and Expenditure. There’s a link to a PDF here.
Adam P: Nick is saying that NK requires agents to have consistent expectations for aggregate expenditures and income, right now. He is specifically not objecting to the hypothesis that AE and Y will be equal at all points in the future. In reality, agents have some expectations about their own future expenditures and income (which of course are not equal), but it is quite a stretch to imagine that the sum of their individual expenditure expectations will be equal to the sum of their individual income expectations. This would be required since the sum of their expectations is equal to the expectation of the sum.
Andy: Yes. “Optimisation condition” is what I should have said. It’s what I “really meant”. It makes my point clearer. I have changed the post.
Scott: yes, it’s not in the Mankiw that I teach too (though there is a discussion of the multiplier process).
“Also, is there any data suggesting that at some points in time aggregate planned expenditure differs from aggregate planned income?”
In Cuba, the line-ups of disappointed buyers are a case where AE greater than Y. In Canada and the US, unplanned inventory accumulation or decumulation would be the data I would point to. But neither is really “data”, since we don’t directly observe plans. But the AE=Y condition is really just the macro equivalent of quantity demanded = quantity produced at the micro level. Prices (or something) needs to adjust to make it happen. It doesn’t just happen by itself. They aren’t identically equal.
Ian: Say’s Law gets defined a lot of different ways. AE=Y=Ys with identities would be one way. I have ignored the supply-side here, since NK’s don’t assert that we are always on the AS curve. AE=Y with identity is just one of the ways “Say’s Law” gets bandied about. Yep, it deserves a fuller discussion. I went deeper into it in some old posts. It’s a bit of a rhetorical flourish here.
Josh: Yep. You need more than constrained optimisation. You need some sort of story, at least, to say how the individual plans that result from constrained optimisation are made mutually consistent.
Travis: the fresh-water micro story would be subject to the exact same criticisms I made here, and then some. (As Adam P correctly noted in the past.)
K: Yep. Better answer to Scott than mine. Expectations and plans aren’t made mutually consistent by magic.
Patrick: ” Would the budget constraint bring everyone into line?”
That’s something I was mulling over. In a 2-period model, with no money, if you are planning to consume your income in this period (and something adjusts this period to make that true) then you must be planning to consume your income next period too, just from the budget constraint. But in a multiperiod model, with money, it can’t work for each and every future period.
Adam: For “AE” read “desired C” or “quantity of consumption goods demanded”. And ignore I, G, and X-M for simplicity. Pure consumption economy. And I’m not worried about whether we can aggregate the Euler equations, or linearisation.
Current income (or interest rate) adjusts to bring current aggregate planned consumption equal to current income. No problem. But what adjusts today to bring current aggregate planned future consumption equal to current aggregate expected future income, for each and every future time period?
Priapus: Neither. No economist (to my knowledge) has ever said the goal of economics is to maximise profits. To oversimplify massively, all economists I know say our goal is to maximise people’s utility. You have a VERY weird and misinformed view of economics. And you are way off topic.
Peter T: sorry. That’s leading us too far afield. The fact that we sell or buy home-produced goods, for example, doesn’t mean demand can’t equal supply. Prices can adjust, if there’s a price.
“But what adjusts today to bring current aggregate planned future consumption equal to current aggregate expected future income, for each and every future time period?”
what needs to? Answer: nothing.
Kevin: there’s the “empirical version of Say’s Law” which says that prices adjust quickly enough so that aggregate supply is always equal to aggregate demand, even though they are not identically equal. There’s nothing logically wrong with Say’s Law defined that way, and freshwater models assume it is true.
K: Thank God! Someone understands what I’m saying, and thinks I might be right!
“Nick is saying that NK requires agents to have consistent expectations for aggregate expenditures and income, right now.”
No, the model does not require this at all.
If, in aggregate, our rationally expecting agents have planned to save a postitive amount next period given today’s income and real rate and their expectations of next periods real rate nothing goes wrong with the model. Tomorrow arrives, the CB observes to little demand and cuts the real rate, driving AE up. Rational expectations don’t always have to be correct expectations.
Now, in steady state equilibrium (a stronger condition than just equilibrium) this doesn’t actually happen but the model can be in a rational expectations equilibrium without being in steady state.
Adam: but if they are not equal, why do NK macro models use the same symbol for both?
They don’t.
I agree – they do not.
Nick, in any macro model the reduced form equations can’t be taken as behavioural relations. That, in large part, is the Lucas critique.
The reduced form model has Y and not C but that has imposed equilibrium conditions already. You can’t study the out of equilibrium behaviour with the reduced form.
This goes back to our other NK debates, the things that drive the return to full-employment are all absent from the reduced form of the model (recall I was talking about firms demand curves and labour supply curves). The reduced form has already imposed the result that we return to full employment eventually, thus you can’t use the reduced form to see how it happens.
Adam and Andy: They do too! A sample of one, but it’s the last NK paper I read (the Bullard and Cho paper himaginary linked http://papers.ssrn.com/sol3/papers.cfm?abstract_id=477821 )
He writes down a standard NK Euler equation, with “Zd” as “deviation of output from trend”. The deviation bit obviously doesn’t matter. It should be “output demanded“, not output. There is no distinction between output and output demanded. There’s only one variable, Z, for both.
Adam: what I am saying is that the reduced form equation for current output is wrong. It would only be correct if currently planned future consumption were equal, in aggregate, to currently expected future income, for all future periods. And there is no reason to believe they will be equal.
I don’t want to pick on the Bullard and Cho paper, first because it’s a very good paper, and second because they are not alone. But it’s actually easier to see the mistake when it’s in their paper, precisely because they do not assume RE for expected future output.
Nick, virtually everyone goes straight to the reduced form. That doesn’t mean it’s not reduced form.
The equation for current output is perfectly fine. The expectation of future output is not any one agent’s expectation, it is the physical expectation. It accounts for the fact that something will adjust to make C = Y, agents don’t need to expect it (although rationally expecting agents do expect this).
If agents, in aggregate are planning to spend 105 on consumption (in all states say) by borrowing (say income is expected to be 100) then there are two possibilities. Either income will rise to 105 or the CB will raise rates and make them happy to spend 100 (say because real expenditure of 105 will be inflationary, let’s ignore combinations of both). Now, agents may not know which outcome will obtain but the model determines it already today (since the model knows the NKPC).
So, if the outcome is going to be that the CB raises rates and AE will come out at 100 in all states of the world then how is it not correct that the expected value of Y is 100?
Here is what I consider a ‘typical’ NK paper: Eggertson-Woodford (2003) (http://www.newyorkfed.org/research/economists/eggertsson/BrookingsPaper.pdf)
Consumers have an Euler equation with C and no Y. Only by imposing rat-ex equilibrium are they able to substitute Y into the representative agent FOCs. That is, equation (2) is a reduced-form relationship with equilibrium imposed. They do it fast and without a discussion, but it’s there.
I have not read Bullard and Cho’s paper, and cannot spare the time at present, but after a quick glance I note that their equations (1) and (2) are linearized approximations to a steady state equilibrium. They are not merely the FOCs/Euler Equations of the consumers’ problem.
yes, what Andy said.
PS: and of course, imposing rat-ex equilibrium allows them to replace indiviual agent’s expectations with the physical expectation. This substitution is basically the same as substituting Y for C.
But just because the canonical model has rat-ex does not mean it needs rat-ex. The Evans video posted by Thoma shows this.
Andy: look at page 149 equation 2 of that Eggertson and Woodford paper. They have Yt and Et[Y(t+1)] in the Euler equation, and they clearly define Yt as aggregate demand, so it’s my AEt, as it should be. It’s not output. But they use the same symbol y (only lower case, because it’s an individual firm) for output in the production function. In other words, they are using the same symbol Yt for both output (income) and desired aggregate expenditure.
“Optimal timing of household expenditure requires that aggregate demand Y, for the composite good satisfy an Euler equation of the form..”
Does New Keynesian macroeconomics lack consistent microfoundations, or does it lack consistent microfoundations that assume every single individual has perfect rationality, perfect information, all the expertise necessary to analyze that information perfectly even though it may take decades to obtain that expertise which is not in few people’s careers, so on top of all the other work they already have to do, and with already a severe lack of time to spend with their families, the necessary incentives to make it worth it to spend all that time (if it even exists in a 24 hour day) to get all that expertise and info and to then do the necessary analysis constantly, and the self discipline to do that even if it were worth the time and enough time existed?
My guess is that George Evans may be immune to my criticism of NK. I would need to read his papers carefully to know for sure.
No Nick, what Evans shows is that the standard NK model is immune to your criticism. Evans takes the same model, without rat-ex, and shows nothing goes wrong. You still converge, under adaptive learning, to the same steady-state. The equilibrium conditions are all the same.
And Nick, on page 149 equation 2 the authors refer to that in the footnote as an equlibrium condition. This condition is derived from the household problem on pg148 (not numbered) and budget constraint (on pg.149, also not numbered).
(And what about my comment from 12:20?)
Richard: yeah, it’s the second. But suppose you asked a NK macroeconomist why current AD equals current output? He would talk about imperfectly competitive firms choosing to adjust output to meet demand if they discovered they were different, because P greater than MC, and maybe say something about inventories etc. He wouldn’t just say “because of rational expectations”. But they can’t give this same answer if we are talking about currently expected future AD and output.
“But they can’t give this same answer if we are talking about currently expected future AD and output.”
are you actually reading the comments?
Adam @12.20: If agents are currently planning to spend $105 next year in aggregate, and currently expecting $100 income in aggregate, there is absolutely nothing that would tell them this year that those plans and expectations for next year are inconsistent. They don’t know other people’s plans or expectations. They don’t know the aggregate plans and expectations. They don’t know that the central bank will need to raise r, or that Y will increase if it doesn’t. They are, as individuals, blissfully aware that their plans and expectations for the future don’t add up.
They are like 105 people planning today to go to a concert tomorrow that only seats 100, and planning to buy tickets at the door. They might know that you can’t seat 105 people in a 100 seat venue. But they don’t know today that 5 people are going to be disappointed tomorrow. If they had to buy tickets in advance, they would discover this today. But without a futures market in seats, they do stuff today that they wouldn’t be doing if they knew that 5 people were going to get stiffed. My accusation is that the NK model assumes that 5 of them will be buying CDs today, because they know they won’t get seats tomorrow.
My concert analogy isn’t perfect, of course, because NK concerts have flexible seating.
Yes, and this is not a problem for the model!
Nor does it make the New Keynsian IS equation wrong!
IF 105 PEOPLE PLAN TO GO TO A CONCERT WITH 100 SEATS THEN SURELY THE EXPECTED (OBJECTIVE DISTRIBUTION) NUMBER OF ATTENDEES IS 100!!!!!
That’s all the equation is saying, it imposes the market clearing condition.
like I said, did you read the 12:20 comment?
Nick, Scott
Mankiw “macroeconomics” 7ed, p 299
the Keynesean Cross
More importantly, they have flexible pricing of the seating.
Ratex versions assume that prices or plans would have to adjust. Excess demand violates equilibria conditions.
Learning models assume that 5 people miss out and people update then they only go for 104, and then 103, etc. You still get to the ratex equilibrium, it just takes some time.
While Adam P. appears to be quite worked up, I must say I share a little of his frustration. Market clearing and feasibility conditions are some of the most basic building blocks of all economic models. I see nothing strange or bizarre in imposing them quickly and without elaborate discussion.
We can have models where people are correct or incorrect about their beliefs about these conditions. That’s fine, we have both of those models. But the conditions themselves are still very straightforward.
I’m not really worked up, I just don’t know how else to indicate extra emphasis in blog comments. (Don’t know how to put italics for example.) And in this case I’m trying to put a lot of emphasis on particular points.
Nick, to make the concert analogy work you’d have to assume that all 100 seats have different owners and only some owners (say 20) show up at the concert to sell their tickets auction style to the highest bidder. The other 80 leave their tickets at the box office to be sold at the posted price. (We could think of the 20 who show up as scalpers).
If 105 people show up looking to buy tickets then the 20 who showed up in person to auction their tickets will charge a higher price, high enough that 5 people will end up happy to go home without seeing the concert.
Andy, as an aside, my understanding of the model is more that ratex vs learning comes in the prices posted by the 80 sellers who don’t show up to sell their ticket auction style.
Ratex assumes that they know what price to charge so that they will get the same price as the scalpers.
Learning means that for some periods the posted prices are too low and the scalpers earn an excess profit but soon everyone figures out what price to post to clear the market, at that point we have the ratex solution where the posted price is the same as the sclaper’s price.
@Adam, I can’t see an obvious reason why learning would happen only through pricing mistakes versus quantity mistakes, mostly because one can quickly go between one and the other. In the original analogy, I was treating pricing as constant and having demand change. Your story makes sense to me as well.
Although I admit I get lost quickly in these analogies because, unlike the math, it’s not clear what is allowed to change and what isn’t, or what consumers are maximizing exactly. It’s too easy to tell sensible sounding stories that have logical flaws when you try to formalize.
Andy, on your second paragraph I agree 100%. Nonetheless, this being a blog and we’re on a first name only basis so…
Basically my point was that within period utility is all about your utility function. If the ticket is priced so you want to buy it today then you’ll try to. I guess your expectations of future prices come into play but the interest rate will adjust to make sure you want to neither borrow or save (that is the representative agent, individuals of course can save or dis-save).
So within period whether you try to buy a ticket, and how much you’ll bid is determined by your utility function. We settle into steady-state when sellers have learned to post the right price so that what they ask at the box office will be the same price that clears the market for the scalpers.
Yeah, I agree with all that. I think I was focused on the dynamics of the analogy. I thought agents were saving to go to theater, but then ‘oversaved’ because they misforecast the demand for seats in a period. Aggregate mistakes like that can lead to ‘incorrect’ interest rates in learning models, and the question is thus whether the economy correctly learns over time. As Evans (and others) show, we should be optimistic about convergence, at least to some equilibria.
This oversaving, of course, cannot occur in ratex models, or at least not in expectations. Whether the adjustment occurs in in interest rates, or only in ticket pricing, or wherever is not very well defined because we’re stuck in Analogy Land.
Also, lol at “first name basis only”. Isn’t it usually the other way?
Andy and Adam: the main point in my post is that the RE assumption, applied to aggregate planned future expenditure being equal to expected future aggregate income, is not credible.
But let me give you an example where my point applies even under RE.
Suppose we have an NK model of consumer-producers (no firms). Haircut economy. Imperfect competition.
There are two sorts of shocks to demand:
Aggregate shocks, which are purely transitory.
Producer-specific shocks, which are purely permanent. (The haircuts I sell are permanently more popular). Uncorrelated across agents, and large number of agents. So they sum to zero in aggregate.
Under full information, if agents could distinguish the two shocks, aggregate consumption would be white noise, and individual consumption would follow a random walk.
Now suppose agents can’t distinguish the shocks, so face a signal-processing problem. And suppose the central bank observes aggregate shocks with a one-period lag, so can’t adjust interest rates quickly enough in response. (This is just to stop agents learning the aggregate shock from the interest rate, and could be dropped in a more sophisticated model with more shocks).
Suppose an aggregate $10 per agent shock hits. Agents think it’s partly individual-specific, and therefore each adjusts upwards his expectation of permanent income by (say) $5. Each plans to consume $5 more today and $5 more next year. Even though each agent, having full-blown RE, knows that expected aggregate consumption for next year is unchanged. And if they knew it were an aggregate shock they would increase current consumption by less.
Aggregate planned future consumption has increased by $5. Expected future aggregate consumption is unchanged.
A model of this economy which failed to distinguish aggregate expected next year’s consumption from expected next year’s aggregate consumption would mis-specify the current demand function. Because they aren’t equal in this case. So it matters which one you put in the representative agent Euler equation. (This is essentially what K said above, I think).
Yep. It’s like in the Lucas 72 model, where the “represntative agent” believes something he knows is logically impossible — that all prices are greater than average. Because the average agent’s belief about his selling price exceeds the average agents’ belief about average selling prices.
You don’t just need RE to put expected aggregate future income in the Euler equation. You need RE plus common current information, so everyone knows what anyone knows. Back to Hayek, and the Use of Knowledge in Society.
Hi Nick,
I’m a long time reader, and first time commenter. I also agree with your critique of the NK model. I found a problem when looking at the liquidity trap with backwards looking expectations. I hope the long post that follows is not wrong, but I am happy with the logic and feel I am getting at the same point as you. I guess the general point is, why are we restricting the consumer’s behaviour using his expectations of future output? He is just one small buyer in the market, and total output should not affect his buying decisions at all, the only thing that should is the price. The practice of equating E[C(t+1)] = E[X(t+1)] violates this.
I started with the IS curve:
X(t) = E[X(t+1)] – const * (i(t) – E[inf(t+1)]) + shock
X(t) here is the unified demand / output notation, and const is some constant. I will use C(t) to refer to effective demand. We are in the liquidity trap, so let the nominal interest rate be zero:
X(t) = E[X(t+1)] + const*E[inf(t+1)] + shock
Now assume that consumers have backwards looking expectations (adaptive, naive etc) for both total output and inflation. Now both of the expectation terms are fixed. Now it looks like current output is completely fixed at some value by these expectations and the shock. So far, so good. Now consider an increase in the money supply in the current period.
We know that if we hand the consumer an some extra income he will want to spread spending it over all future periods. That is, he wants to increase both C(t) and E[C(t+1)]. But the IS equation does not allow this – X(t) is fixed. So by this logic an increase in the money supply is not spent, and we appear to be in a liquidity trap. But this cannot be the case because it violates the consumer’s money demand equation – a change in real money balances with no change in interest rates or output means that the consumer has excess money balances. Why has the increase in the money supply not increased demand? Something is wrong.
Our logic about what the consumer wants to do with his extra money implies that C(t) and E[C(t+1)] increase. But the NK practice of equating E[C(t+1)] and E[X(t+1)] does a strange thing: it does not allow E[C(t+1)] to increase, because E[X(t+1)] is fixed by adaptive expectations. Thus an internal contradiction arises in the model – if we accept E[C(t+1)] = E[X(t+1)] an increase in the money supply at the lower bound does not increase output but in doing so violates money demand.
The alternative is that we allow the increase in the money supply to increase output – we suppose the liquidity trap does not exist with adaptive expectations. In this case we allow the increase in the money supply to increase the consumers current and future demand, C(t) and E[C(t+1)]. The increase in current demand increases current output: C(t) = X(t) and we can stop the money demand equation from being violated. But, to do this we have to allow that E[C(t+1)] changes so that we satisfy the consumer’s Euler equation. But, to do this we have to acknowledge that E[C(t+1)] no longer equals E[X(t+1)].
What do you guys think? Am I making sense, or am I wide off the mark? I am happy to be corrected.
Adam P – the point you make about the reduced form imposing the return to equilibrium is really interesting. Could you please point me in the direction of a discussion about that? I would love to learn more.
In the model I have sketched out in the above two comments, aggregate output will fluctuate, but the fluctuations will be white noise, so Et[Y(t+1)] will be a constant. That’s because the central bank responds perfectly to stabilise output, but only with a 1 year lag.
But the representative agent will see shocks to his Y(t) as being partly permanent, so the Et[Y(t+1)] that belongs in the representative agent’s Euler equation will not be constant, and will be positively correlated with Y(t).
The implication is that exogenous demand shocks will have a bigger effect on Y(t) than they would if agents could distinguish aggregate from producer-specific shocks.
And a misspecified Euler equation, which held Et[Y(t+1)] constant, would underestimate the size of aggregate fluctuations caused by exogenous shocks to demand.
Hi brit, and welcome!
What you are saying makes partial sense to me. In the individual experiment, an agent’s current demand is a function of the interest rate and his expected permanent income, both of which are exogenous to the agent, in a world where output is demand-constrained, which is the canonical NK world. And if some shock (like a monetary injection, or whatever) increases his planned consumption path for all periods, that doesn’t mean it increases his expectation of permanent income from the sale of newly-produced goods. It would only increase his expected permanent income if he knows that all people have received the same helicopter drop of money (or whatever), and so all people will be raising their planned consumption paths likewise, and so will be buying more of the goods that he sells. An excess supply of money, so every individual tries to get rid of it by spending more than he gets in income, is exactly a case where permanent planned consumption exceeds expected permanent income for the representative agent. Money is a hot potato. Each person tries to get rid of it. Each individual can get rid of it, by spending more than he earns. But in aggregate they can’t get rid of it. Their plans and expectations are not mutually compatible.