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"The representative agent cannot be assumed to know he is the representative agent. He observes the shocks that hit him, but does not observe the shocks that hit other agents. He cannot distinguish individual-specific from economy-wide shocks."

The representative agent cannot be assumed to know that the is the representative agent, but he cannot be assumed not to know, either. In this day of widespread communications, the representative agent is very likely to be aware of economy-wide shocks. "And we get our news like lightnin', On the telegraphic wires." -- 19th century song

Min: true. But what matters is how his knowledge compares to the central bank's. Only if he were certain the Bank knew nothing he didn't know (i.e. if he knew the Bank's knowledge was a subset of his own knowledge) would he be able to say with certainty: "The Governor's hand trembled on the nominal interest rate lever". Otherwise, he faces a Lucasian signal-processing problem, where his estimate of the natural rate is a weighted average of his own knowledge and the nominal interest rate set by the Bank, in which case we get qualitatively the same results as in my second case.

Stephen Williamson has a new post:


Mark: thanks, yes, I saw it. He loses me at equation 1. I interpret that equation as saying what the (expected) inflation rate *would need to be* to keep output at potential, rather than what (expected) inflation *would actually be*. And if (expected) inflation fell below that number, the real interest rate would be too high, so there would be excess supply of goods, so actual and expected inflation would fall still further.

In other words, I found David's post more of a challenge to my way of thinking than Steve's. David's post forced me to think and then write this post. Steve's new post is the same as his old one. He clarifies the equilibrium a bit more, but that's it. In the words of an Old Keynesian: "He just assumes full-employment!"

Nick: "The representative agent cannot be assumed to know he is the representative agent."

Is that the conventional understanding of RatEx as applied to macro? I'm asking since I've assumed the opposite to be the case for the last 30 years at least. AFAICT the usual assumption (Lucas '72 is not at all typical) is that the agent knows all there is to be knowed. Indeed most models would be utterly impossible to solve, if the representative agent doesn't know what other agents are going to do.

Kevin: I think you are right. I don't think it is conventional thinking. But I'm not 100% sure.

It is so easy to slip from: "Each agent knows everything about his own preferences and technology" (a reasonable assumption) to "The representative agent knows the representative agent's preferences and technology" (which sounds like the same thing, but in fact would only be true if the representative agent knew he was the representative agent, which would only be true if he knew every agent's preferences and technology).

I wonder if they have even thought about it? But you can see the second assumption being made implicitly in the papers that David cites. The agents are assumed to know the natural rate.

Interesting post Nick.

On first reading I think you've got right to the heart of the debate and I think you're largely correct. However, a nit-pick follows.

You need to strenghten

"The representative agent cannot be assumed to know he is the representative agent"


"The representative agent cannot know he is the representative agent"

It's not possible for the representative agent to know he's the representative agent because he's not a single person, the representative agent is NOT simply one of the agents chosen to stand in as "representative".

Representative agent ~= typical agent. ( ~= is "not equal").

Actually forget the nit-pick. As I re-read I see that this is exactly what you're saying.

Thanks Adam! Yep, we can *imagine* a world in which the representative agent does know he is the representative agent. Like if every agent knows everything about every agent, and there just happened by fluke always to be a single agent who was a perfect composite of all the agents. Or all agents are identical and every agent knows that. But it's not a reasonable assumption, in most cases.

Noah Smith:
“Williamson’s model, if I’m not mistaken, predicts that QE will cause a short burst of slightly higher inflation, followed by a long period of lower inflation.”


Alas, I believe Noah Smith is mistaken.

On page 14 of Stephen Williamson’s paper, equation 40 states that the gross inflation rate is given by:


Where Mu is the gross inflation rate, Beta is the discount factor bound between 0 and 1, x1 is the amount of currency and u is a a strictly increasing, strictly concave, and twice continuously differentiable function.


Thus an increase in the amount of currency strictly decreases the inflation rate. In my reading of his paper this appears to be true regardless of whether the central bank is operating a channel or a floor system, regardless of the maturity of the debt it purchases, and whether it is at or away from the zero lower bound.

On page 16, in the section on conventional open market operations in short-maturity debt, he notes:

“Some of the effects here are unconventional. While the decline in nominal bond yields looks like the “monetary easing” associated with an open market purchase, the reduction in real bond yields that comes with this is permanent, and the infl‡ation rate declines permanently. Conventionally-studied channels for monetary easing typically work through temporary declines in real interest rates and increases in the in‡flation rate. What is going on here? The change in monetary policy that occurs here is a permanent increase in the size of the central bank’s holdings of short-maturity government debt – in real terms – which must be …financed by an increase in the real quantity of currency held by the public. To induce people to hold more currency, its return must rise, so the in‡flation rate must fall…”

> He raises his price by 2%, but with the real interest rate now higher, he cuts his own current consumption and investment.

Is this possible? Until income effects percolate through the system (experienced in the next paragraph as a demand shock), how can an agent simultaneously decrease consumption and investment?

If the agent holds cash, then it's profitable to hold bonds instead (that offer a positive real return), and we're back to investment. If the agent holds excess bank reserves, then when we're not at the ZLB those still don't pay interest and we're back to "hold bonds instead."

What it can do is affect an agent's expressed time preference. If the agent believes that the rate hike does not represent a real change of interest rates, then the agent's preferred path of consumption remains unchanged: r(t) - n(t) remains fixed in your hybrid model.

If the agent believes that the rate hike represents an increase in the real interest rate (due to an "overheated economy"-type monetary adjustment), then the agent will believe that r(t) - n(t) has increased, causing an increase in preference for Cdot(t). The only way to satisfy that is by a jump decrease in C(t) with a corresponding increase in investment/savings in instruments that return that r(t).


Naturally you caught me during FOMC, so I have to drop this potato for the moment.

What this post is all about, in my view, is an expression of your preferred model -- your preferred way of interpreting the macroeconomic world around us. I think it is a perfectly legitimate view! But it is only one out of many other possible interpretations (no matter how implausible you think these competing interpretations are). It certainly does not follow that SW should have his union card revoked, or that many in the profession have "lost their way" because they do not subscribe to this particular view.


Hayek's thesis is wrong. He says statistics is not good for novel and fleet-brained problems, which is fine. He is sketching out some sort of lateral thinking or logic speed-test competancy, which should be a pre-requisite of industrial/economic power. This is fine. But then Hayek says only those with local infomration should for economic/industrial power. This is false. This position is only tenable before WWI. After military and industrial advances enable mass murder and mass control, we need actors with good ethics and the problem solving ability and environment/nature that yields good ethics. Hayek is only saying that putting rich industrialists in charge of society is better than having Soviet communism consumer markets. Probably about 1000 rational agents have wanted to nuke USA, EU, UK or Israeli cities. There are many rational agents in North America trying to bring aobut AGW revelations. And there are many future risks, that will only be solved by ignoring market forces.

For starters, if I were a central banker, I'd send out a survey using Stats Canada, and I'd wait recipient responses higher if they were part of one or more past recessions, if they accrued their wealth using business or technological (in oppoisiotn to the Hayek paper) acuman, if they ascribed to stakeholder theories (which biz school I guess), and I'd ask these recipient about their thoughts of hiking an interest rate. With telephones, mobile devices, computer databases, his Cold war thesis no longer applies. His disdain for science and engineering is laughable. The paper isn't economics. It belong in the Bible is so polemical. It is a rich and powerful child writing that he wishes neighbourly small business entrepreneurs made good commanders in chief.

Down the rabbit hole of rational expectations? If the bank is lowering rates, I had better save even more for the coming apocalypse, and when I manage to save less, I must redouble my efforts for I am now sure it is coming, and when they raise rates it is because better times are coming and I can save less. It is pretty easy to come up with a counter story for my preferred actions. What is the bank saying? Should I believe them or not? Are they shielding me from the truth or underestimating it? Should I panic before everyone else does or hold steady when everyone else does? How will my actions affect the bank and how should the banks actions affect me? Will the bank over or under correct? Will I over or under react? Will I even react in the direction expected? His story seems to be one where agents react perversely, perhaps out of distrust, expectations worsening and compounding, rising fear and risk premia.

Krugman's response is here: http://krugman.blogs.nytimes.com/2013/12/02/immaculate-stability-wonkish/

He makes a point of distinguishing the Dornbusch type models of excahnge rate determination from what Williamson is doing. I'm curious if Nick or others here gree that this distinction is legitimate?

It seems to me that Dornbusch-Krugman models are vulnerable to exactly the same criticism that Nick makes of Williamson here. If I find that bonds in a currency A have a lower yield than comparable bonds denominated in other currencies, I sell them. This leads to a depreciation of currency A, which lowers the return on A-denominated bonds, which leads to further selling. The only way you get the exchange-rate dynamics the model describes is if everyone already knows the fundamentals-determined equilibrium exchange rates, AND the exact date at which market rates will return to those equilibrium. As soon as you relax the assumption that people's beliefs about the exchange rate at a future date are completely independent of the current level of the exchange rate, the equilibrium is no longer stable. Am I wrong to think this?

It seems to me that the problem faced by people like Krugman, Wren-Lewis, etc. is that the models they have been using and teaching for the past 25 years do not support their policy preferences or their view of how the economy really works. And now they are mad that people are taking what they've been saying seriously.

"...OK, so “agents require” a fall in the inflation rate to induce them to hold more currency. How does this requirement translate into an incentive for producers of goods and services — remember, we’re talking about stuff going on in the real economy — to raise prices less or cut them? Don’t retreat behind a screen of math — tell me a story.

I don’t think either Andolfatto or Williamson have any such story in mind; they are, in some form, invoking the doctrine of immaculate inflation. And I don’t even think they realize that they have a problem..."


You know, I don't even really mind that there isn't a coherent story (unless you honestly think "agents require a fall in the inflation rate to induce them to hold more currency" is coherent). What I object to is the fact that nobody defending Williamson's model both realizes that this is what the model actually claims, and can simultaneously point to clear empirical evidence of this actually happening in real life.

> If I find that bonds in a currency A have a lower yield than comparable bonds denominated in other currencies, I sell them. This leads to a depreciation of currency A, which lowers the return on A-denominated bonds, which leads to further selling.

I'm not sure that's entirely a problem? At some point, the purchasing power of currency A with respect to B will change such that it will be profitable to purchase real property in currency A, transport it to country B, and sell it for currency B at a profit. Purchasing power parity provides the medium to long term control over currency prices, while differential bond yields informs the shorter term change in those yields.


Yes, that is the logic of old-fashioned ISLMBP models. A feature of those models is that the interest-parity condition does NOT hold: It is possible for interest rate differentials to persist indefinitely, without offsetting exchange rate changes, provided that current account surpluses in the low-interest countries are large enough to offset their financial outflows.

But Krugman explicitly rejects this idea. If you pick up his undergraduate textbook on International Economics, you will find that he is fully committed to a Dornbusch-style story in which interest parity holds continuously and net financial flows passively adjust to the current account balance. There is not even a hint of the story you're suggesting, which was the mainstay of older textbooks.

David: have fun at the FOMC! Look forward to your return.

JW: " As soon as you relax the assumption that people's beliefs about the exchange rate at a future date are completely independent of the current level of the exchange rate, the equilibrium is no longer stable. Am I wrong to think this?"

Not obviously wrong, but not obviously right either. Wouldn't it depend on *how much* expectations of the future exchange rate depend upon the current exchange rate? And wouldn't that depend on what they thought had caused the initial depreciation? (I am more and more coming to the view that Scott Sumner was right all along in "Never reason from a price change". Just as we economists shouldn't do it, we shouldn't assume economic agents do it either. They will want to know the reason why it changed.)

Mark: "You know, I don't even really mind that there isn't a coherent story (unless you honestly think "agents require a fall in the inflation rate to induce them to hold more currency" is coherent)."

I mind. The argument from design looks pretty good too, empirically. And if we allow ourselves to adopt Functionalist models here, that begs the question of why functionalist models are OK here but not OK in other applications, where they fall flat empirically because of the free-rider problem.

...I'm thinking of a GAI for the middle class up if they reveal their human capital (what they read and the human capital of who they communicate with), and leave themselves on a Crown telemarketer list. If you base your central banker decisions on human capital you will do better than a Soviet system or picking whoever gets compund interest or leverage with their past possibly-efficient-then earning....more nodes of power is good to prevent tyranny. Coyne Sr and the Senate both acted to prevent PM tyranny, decades ago. Incremental Banker activities such as inflation shifts, like carbon shifts work for GHGs and the executive, are the correct response to new tools and central banker experiments. The problem with the Egyptians was they turned into a bureacracy of copying written laws of past leaders. Hayek is being eaten by worms. Let's forget about him.


It seems to me that the problem faced by people like Krugman, Wren-Lewis, etc. is that the models they have been using and teaching for the past 25 years do not support their policy preferences or their view of how the economy really works. And now they are mad that people are taking what they've been saying seriously.

IMO people like Krugman are genuinely interested in how the economy works and spend a lot of time trying to figure this out, so they think of a story and then write down a model to see if the story is consistent. The definition of "consistent" as commonly accepted does not include "robust", which you are perhaps arguing it should. That is common sense except it is very hard to define "robust" rigorously; it's not just about stability and often stability questions are more difficult to answer than finding an equilibrium in the first place. The model is one piece of evidence that their story is not immediately ruled out based on pure logic.

On the other hand, Williamson and others *pretend* to argue from the model -- spinning a story about what the model "tells us". The problem is that most models are wrong on almost every count, because the set of consistent models is much larger than the set of accurate models. Therefore arguing from the model requires convincing proof that the model is accurate, for whatever policy purpose is planned, in addition to being internally consistent.

But I do not believe that Williamson is really arguing from a model as he seems like an intelligent person. He must *really* be arguing from a story, but does not want to lay out his story, either because the story is not very convincing or because he doesn't really want to think through the implications of the story (which is different than thinking through the methods of solving a model).

It is not an accident that people like Williamson dismiss the long discursive essays of economists in the past -- thinking through a story, to see if it makes sense -- is just as difficult, requires just as much time and concentration, and is not more prone to error when attempting to prescribe policy advise than solving a stochastic optimization problem.

Anyone from Downunder who has been following monetary policy will agree completely that it matters why folk think the Central Bank did it. Because the RBA has an implicit price target, people read its interest rates shifts differently than, say, the ECB. Interest rates are a signal within a policy regime. Different policy regimes mean different signals.

That should read "implicit income target".

Consider a single bank in a competitive banking system. It decides to expand its balance sheet,
purchasing long term bonds. Call that "quantitative easing." It finances the purchase of bonds by
issuing monetary liabilities. The quantity of those expand, lowering their liquidity premium. To get
people to hold them, it must pay a higher real interest rate on them. For deposit type monetary liabilities
this can be accomplished by paying a higher nominal interest rate on them.

Suppose that the monetary liabilities take the form of hand-to-hand currency. It is too difficult to pay nominal
interest and so it is zero. The way to raise the real interest rate is cause "deflation." For the single bank
that is done by appreciating the exchange rate relative to other bank liabilities. For all banks, it is a bit more
challenging. It would involve promising to appreciate all the currencies relative to goods--promising deflation.

If the bank chooses to expand its balance sheet by purchasing long term bonds, it must increase the rate at which its currency appreciates.
This results in a higher deflation rate in terms of goods and services. How will those using the bank's currency know about this? Presumably the same way they would know that the nominal interest rate was increasing with deposit type monetary liabilities. The bank would tell them.

What happens if the bank fails to increase the nominal yield on its deposit-type liabilities enough to cause people to be willing to hold the greater quantity despite the lower liquidity premium? In a competitive system, the bank suffers adverse clearings.

What about where the bank fails to appreciate its zero-nominal yield currency enough to create the sufficiently high real yield? Again, adverse net clearings.

Now, what if the exchange rates between different bank monies isn't fixed at par or at some increasing peg, but rather floats? The adverse net clearings implies a currency depreciation and inflation of the bank's liabilities relative to goods and services.

If the private monetary arrangements are too arcane, suppose rather than a bank, it is a small open economy with a fixed exchange rate. The bank of Canada purchases mortgage backed securities to funnel credit into housing. It funds this by issuing monetary liabilities. It can pay higher interest on deposit type liabilities. But if it wants to keep the nominal interest rate on those liabilities low, and also increase the real yield on hand-to-hand currency, it can generate deflation. It could do this by appreciating its currency relative to the U.S. dollar. In days of yore, it could do the same with gold. Of course, it would announce that it is doing this. The whole point is to raise the demand for the monetary liabilities.

What if the Bank of Canada failed to raise the interest rate on deposit type liabilities or increase the dollar peg, and increase the quantity of monetary liabilities anyway. The result would be higher inflation. Considering exchange rates, excess Canadian dollars, with their excessively low yield relative to the low liquidity premium due to the high quantity would be sold for U.S. dollars. The exchange rate falls, and the prices of imported goods rise, resulting in higher inflation.

So his thinking is that creating money makes money worth...more?

That would seem to take care of the debt problem, wouldn't it?

Do you have something like this post on objective and subjective rationality in applied game theory in mind?


"Only if the representative agent knew he was the representative agent would he be able to solve the aggregate version of the central planner's problem, just by introspection and rational expectations."

That's not enough, as the Prisoners' Dilemma illustrates. Let each of the prisoners know the payoffs of the others, so they know that each of them has the same payoffs. Kantian agents could reason that since their payoffs are the same, their strategies are the same. On that assumption it is easy to see that the do best when they both cooperate. But, aside from the fact that few criminals are Kantians, they cannot be sure of the other's actions.

OTOH, we cannot be sure that both would defect, either. We have evidence that college freshmen, asked to play the Prisoners' Dilemma with a complete stranger, cooperate more than they defect. If the rational strategy is to defect, why does a population of naive players do better than a population of defectors? As Axelrod pointed out in "The Evolution of Cooperation", there is really no generally objectively best way to play the Prisoners' Dilemma.

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