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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.

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.

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