Sunday, December 1, 2013

Teachable Moment

Students are often confused, and we can't always figure out why. The teachable moment comes when students actually articulate their confusion, and then you can work on trying to help them. Nick Rowe, Brad DeLong, and Paul Krugman are all confused - each in his own way - about my last blog post.

Let's start with Krugman, as he's by far the most articulate of the lot - you can actually understand what he's complaining about. The basic ideas in my post come from two papers, my recent AER article, and this recent working paper. So, I'm not just writing something in a blog that I thought up in the shower. The models I have been working with are built on a Lagos-Wright base. There are good reasons for that. In particular, including credit, collateral, banking, and other key features of financial markets in this type of environment is relatively straightforward. However, not everyone is familiar with Lagos-Wright, so I took some pains to write up some notes based on cash-in-advance. Why cash-in-advance? I think Krugman understands it, since he is clearly a slavish follower of Bob Lucas, and Paul has used cash-in-advance at least once in a paper.

Krugman should love this, for a number of reasons:

1. The key to solving the inefficiency problem that arises in the model is fiscal policy.
2. The underlying problem is that the fiscal authority is doing something stupid.
3. The economy is non-Ricardian - government debt matters.
4. Monetary policy is non-neutral. Indeed, monetary policy can have effects that persist forever.
5. This is all about financial frictions. During the financial crisis, some people seemed to want to tell macroeconomists they had been barking up the wrong tree by paying insufficient attention to such things.

Indeed, if I wanted to, I could probably find something in these ideas that I could link to Keynes's General Theory, call what I do Neo-New-Keynesianism, and start a new fad.

To summarize what is in my cash-in-advance notes, I assume a simple setup where assets other than money play some role in financial arrangements. It's very hard to do collateral constraints (at least it seemed to me it was) in this environment, so I just assume that there are two kinds of transactions - one where you need money, and another where you can use money and bonds. This is to capture the idea that government debt and other safe assets are useful in financial exchange and as collateral. In an equilibrium in which the value of the consolidated government debt is sufficiently small, asset-in-advance constraints bind, and the low quantity of consolidated government debt tends to make consumption and output low, produces an inefficiency wedge, increases the liquidity premium on government debt, and reduces the real interest rate.

In a liquidity trap equilibrium, where the nominal interest rate is zero and open market operations are irrelevant at the margin, if the value of the consolidated government debt is sufficiently low, the inflation rate i is determined by

(1) i = BW - 1,

where W is an inefficiency wedge related to consumption goods - a financial inefficiency wedge - and B is the discount factor. With no financial inefficiency, W = 1. Further, that inefficiency wedge is what is determining the liquidity premium on government debt at the zero lower bound. That is, the low real interest rate is associated with an inflation rate greater than the rate of time preference at the zero lower bound.

Why is this important? Economists have typically associated the zero lower bound with deflation. Thus, once the Fed effectively went to the zero lower bound in late 2008, some people, including Krugman, started to worry about deflation. But the deflation never appeared - indeed, by mid-2011 the inflation rate was running at close to 3% per year. Krugman, faced with a puzzle, argued that wage rigidity explained why inflation was not falling. But you can explain what is going on more satisfactorily, I think, by taking account of the financial inefficiency wedge. At the zero lower bound, as inefficiency increases, the inflation rate rises, and as inefficiency wanes, the inflation rate decreases. Following a financial crisis, it certainly seems useful to explain what is going on in terms of financial factors, and the post-recession path for the inflation rate in the U.S. seems roughly consistent with the story.

So far, dynamics and "stability" don't enter the story. As I show in my notes, the model is fully dynamic, but it actually solves like a static model. Given the fiscal policy rule, the central bank chooses a nominal interest rate period-by-period, and that gives a unique solution for consumption, output, hours worked, and the real interest rate.

But, we could imagine superimposing some policy rule for the central bank on top of this. That's basically what Krugman is up to. The picture he shows you works under the assumption that the "natural rate of interest," which is also the long-run real interest rate, is a constant. You can find a picture like Krugman's in Jim Bullard's Seven Perils paper. Bullard's paper has a useful discussion of the literature related to Taylor rules and their properties. Various people have worried about whether the Taylor rule will induce dynamics that will lead you to the "bad" steady state with deflation, rather than the "good" steady state in which the central bank hits its inflation target. But that's not the issue here. A key difference in my model is that the steady state real rate of interest is not a constant. It will depend on the financial inefficiency wedge, which is endogenous - in particular the financial inefficiency wedge depends on monetary policy. So, you can't draw a simple picture like Krugman's.

However, we can address Krugman's concern, which is that, if the central bank follows a Taylor rule, and the economy is at the zero lower bound, then some small perturbation will send this economy to the "good" equilibrium. Suppose, for example, a typical linear Taylor rule (multiplicative in my notes, but essentially the same thing) of the form

(2) R = max[ai +(1-a)i* - bg + r, 0],

where a > 1, i* is the central bank's target inflation rate, b > 0, g is the central bank's perceived "output gap" - the difference between what the central banker thinks is efficient output, and actual output - and r is the central banker's perceived "natural rate of interest." Then, using equation (1) to substitute in (2),

(3) R = max[a(-s+w)+(1-a)i*-bg+r,0],

where s is the rate of time preference, and w is the log of the financial inefficiency wedge. We'll have w=0 if the financial inefficiency disappears. So, suppose that the central bank has chosen to be at the zero lower bound, which implies, from (3), that

(4) A = a(-s+w)+(1-a)i*-bg+r <= 0. The central banker has been convinced of the wisdom of New Keynesianism, has been reading Paul Krugman, and is convinced that g is high and r is low - he or she thinks there is a large Keynesian sticky-wage and sticky-price inefficiency gap, and a low natural rate of interest. That's why he or she has chosen to peg the nominal interest rate at zero. Now, suppose that the financial inefficiency wedge falls for a period of time. From (1), the central banker will see a falling rate of inflation. That will act to reduce A and make the central banker want to stay at the zero lower bound. Further, if the central banker is a truly committed New Keynesian, falling inflation will make him or her think (through New-Keynesian Phillips curve logic) that the output gap g is increasing, which makes A fall further. For example, if you were Narayana Kocherlakota, you might say:
These low levels of inflation tell us that monetary policy can be useful in increasing the rate of improvement in the labor market.
Or, put another way,
The underlying deficiency of demand will call for pedal-to-the-medal monetary policy as a norm.
So, there are plenty of good reasons to think that a New Keynesian, living in my model world, could get stuck at the zero lower bound. Under the Taylor rule, the zero lower bound is as stable as a large rock sitting on the open prairie. The quantity A can fluctuate for various reasons, but as long as the inequality (4) holds, the economy stays at the zero lower bound. Note that increasing the inflation target i* does not help, as a>1.

Noteworthy is the fact that the last quote comes from Paul Krugman. He's part of what makes the policy trap a trap.

Three final points:

1. David Andolfatto wonders:
What would the Fed be doing differently if they took this view? Not much, as far as I can see.
A key question is: What's the optimal monetary policy in my model? In my cash-in-advance notes, I'm pretty sure that optimal monetary policy is a zero noiminal interest rate under any conditions. That's basically Friedman-rule logic - inefficiency will be minimized when the nominal interest rate is zero, even if the usual Friedman rule is not feasible, as is the case in my model. There are good reasons to think that the standard Friedman rule - which comes out of many monetary models - is missing something important. I have argued (see my AER paper), that there are various costs associated with paper currency - costs of replacing worn-out notes, counterfeiting, fraud and theft, illegal activities. It's efficient to tax that stuff through inflation. There are cheap ways to capture that in the model, without changing anything of significance. Then, it may be the case we would actually be better off with a higher rate of inflation. But we aren't going to get it because the Fed is caught in a policy trap that will keep us at the zero lower bond indefinitely.

2. Paul Krugman thinks that a paper by George Evans has something to do with what I'm talking about. It doesn't - that's about learning in a New Keynesian model. Also, this doesn't have much to do with Kocherlakota either. Kocherlakota was thinking about the world depicted in Krugman's diagram, where the long-run real interest rate is a constant.

3. Some of Nick Rowe's confusion has to do with some holes in his knowledge of dynamics, I think. When I learned macro as an undergraduate (circa 1975), it was common for people to tell pseudo-dynamic stories in static models, probably because they wanted to make these models seem more realistic. For example, I remember an instructor discussing how monetary policy worked in an off-the-shelf Hicksian IS-LM model. The story went something like: M increases, which happens by way of an open market operation, which makes the price of bonds go up and the interest rate go down in financial markets. This increases the demand by firms for investment goods. They buy those goods from other firms, which then find that their inventories are going down. This causes those firms to increase production, and Y goes up. Of course, there are no inventories in the IS-LM model, and no firms producing anything - that's just a story that my instructor made up to make IS-LM more convincing. Actually, she was just doing comparative statics. There's a unique static equilibrium. M changes, the nature of the equilibrium changes, and we can take some derivatives and determine how it changed. But some people took those stories seriously. For example, those people wanted to make arguments such as: If I have this parameter configuration, then when I do the comparative statics I have trouble telling my pseudo-dynamic story. Therefore, that is a parameter configuration I am going to rule out. I think Nick retains some of that thinking, as you can see in the comments on this post.

48 comments:

  1. Steve: "I think Nick retains some of that thinking, as you can see in the comments on this post."

    Yep. I stand by my comments in that post.

    In this post, you lost me at equation 1. I would interpret that equation as telling us what the (expected) rate of inflation *would need to be* to keep the economy at "full-employment" (potential output/natural rate of output/whatever). It does not tell us what (expected) inflation would *actually* be. And if (expected) inflation were below that level, there would be excess supply of goods, so actual and expected inflation would fall further, which would make the excess supply even worse.

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    1. No, (1) is just an equation that has to hold in equilibrium. No more, nor less. In the model, what is exogenous is: (i) the real value of the outstanding consolidated government debt; (ii) the nominal interest rate. The first is set by the fiscal authority, the second by the central bank. Then, inflation is endogenous, but determinate.

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    2. Steve: just to be sure: you are not invoking the Fiscal Theory of the Price Level, are you? I don't think you are, but wanted to be sure.

      Let me put my argument in Old Keynesian language: you are just assuming full-employment, even though there is nothing in your model that would lead the economy to full employment if it ever started away from full employment. If agents acted in their collective interests to create just the right amount of inflation to keep the economy at full employment, it would stay there, but it is not in the individual interest of any individual agent to create the socially optimal amount of inflation, or to expect others to create the socially optimal amount of inflation. If the central bank announced the socially optimal inflation target, it could work as a Schelling Focal point on which agents could coordinate their beliefs. But there is no mechanism which would lead individual agents towards expecting that socially optimal rate of inflation. They can't learn it from experience.

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    3. If I understood Steve's model when I read it a while back, a bigger financial inefficiency results in greater scarcity for bonds. This should, in turn, lower their real rate of interest. But since the nominal rate of interest is already zero, the only thing that can adjust to bring about the decrease is the inflation rate, which rises as a result. A drop in financial inefficiency has the opposite effect of reducing inflation.

      If I am correct, the question still remains, however, of how the increase in inflation happens in real life. Stories may not be as convincing as formal dynamics, but, if plausible, they certainly help with the argumentation.

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    4. "you are not invoking the Fiscal Theory of the Price Level, are you?"

      It's not that, but yes, the fiscal authority has something to do with determining prices.

      "you are just assuming full-employment..."

      Wrong. In my notes, you can say exactly what "full employment" means. There's a Pareto optimum, and the equilibrium allocation is definitely not that. The suboptimality is that there's not enough consolidated government debt. No coordination problem.

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    5. "Stories may not be as convincing as formal dynamics..."

      No, there is formal dynamics. It's all in there.

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    6. Thanks, I did go over it quickly, guess I have to go back when I have more time, probably during the winter break.

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    7. CA, as I read the model, it's the scarcity of bonds that determines the financial inefficiency. See page 5 of his "notes."

      But there are some other things that don't make sense:

      1. What the heck is the liquidity premium on government bonds? There are only two assets in the model: money and bonds! So the bonds will never have a liquidity premium.

      You can't just hypothesize the existence of less liquid assets without considering their valuation. For instance, a lower supply of safe assets should increase the price of risky assets (which has of course happened in the past two years). Since risky assets can be changed into money (even though they aren't fully liquid, they aren't completely illiquid), more money is available for consumption or collateral. That, in turn, would cause the inefficiency wedge to decrease, contrary to the model's assumptions.

      The model, in fact, does not allow risky assets to be used as collateral. I suppose that's fine, except that risky assets can't flitter in and out of the story as convenient. Either they exist, in which case they can be used as collateral (perhaps at a discount), or they don't, in which case the whole concept of a liquidity premium makes no sense.

      2. There is a point 2 to which I will perhaps return tomorrow. I'm tired now.

      I think Nick Rowe is right. There's too much math, and too little contemplation of the relationship of the math to observed reality.

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    8. Steve: "It's not that, but yes, the fiscal authority has something to do with determining prices."

      OK, I got that. I was just checking my interpretation was correct.

      "There's a Pareto optimum, and the equilibrium allocation is definitely not that. The suboptimality is that there's not enough consolidated government debt."

      OK. I got that too. But given that suboptimal level of government debt, it is as if some benevolent deity were choosing the actual and expected rate of inflation to ensure the Euler equation is satisfied at full-employment output, despite whatever stupid things the central bank do with nominal interest rates. Methodological individualism has been thrown away. There is no story about why individual agents would choose that actual and expected inflation rate. Plus, unless you assume all agents are identical, and know it, there would be no way each individual agent could ever know what actual and expected inflation rate would satisfy the Euler equation at full employment. So they couldn't engage in tacit collusion to ensure the Euler equation is satisfied at full employment even if they wanted to.

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    9. Nick Rowe just hit my point 2, explaining it somewhat differently than I would have. Probably better, although I think it's better to skip the word collusion.

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    10. "The model, in fact, does not allow risky assets to be used as collateral."

      You can add that, and get the same things. See my AER paper.

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    11. " There is no story about why individual agents would choose that actual and expected inflation rate."

      Of course there is. There are optimizing agents in the model, they optimize, and in equilibrium that's what happens.

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    12. Anonymous, I will take a shot at point 1

      My understanding is that the liquidity premium is the difference between the price of the bond that would prevail if it only served as a tool for transforming current consumption to future consumption (e.g. if the rate of interest were equal to the rate of time preference) and the one that prevails when the bond can, in addition, be used as a medium of exchange.

      Also, regarding financial inefficiency, as I understand it this is similar to an increase in the cost of supplying credit. Such an increase reduces the supply of credit, so the demand for liquid assets rises. The problem is that the supply of one of these assets, bonds, is fixed by the level of the government debt. Moreover, since money and bonds at the zero lower bound are practically identical, swapping one for the other through open-market operations is irrelevant.

      Finally, it is true that Steve is a bit short on words, but I am not sure that this signals a lack of contemplation. I have a feeling he is doing it on purpose, sitting behind his computer screen, sipping the beverage of his choice, and enjoying watching people contemplate his work and trying to figure things out on their own. :)

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    13. "Of course there is. There are optimizing agents in the model, they optimize, and in equilibrium that's what happens."

      Steve, that's not an explanation of how the equilibrium is reached. It is a formal re-statement of that equilibrium is reached.

      To put it in terms of Hayek (1945) it's the logic of choice, but the economic problem has been assumed away.

      To put it in terms of Samuelson (1947) it's the reasoning backward from perceiving that land is used in a certain way by a farmer to that the marginal returns for each piece of land must be equal to every other piece of land.

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    14. "Steve, that's not an explanation of how the equilibrium is reached."

      So, suppose I write down a supply curve (upward sloping), and a demand curve (downward sloping) which is supposed to describe the market for apples. What's the story about how equilibrium is reached?

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    15. Re apples:

      Let P* be the equilibrium price.

      Suppose PP*, just swap buyers and sellers.

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    16. Damn! Must use spaces either side of < and >

      Suppose P < P*. There will be excess demand for apples, so some buyers will be rationed.

      An individual seller will realise he can increase his profits by raising his price slightly above P, because the rationed buyers will prefer paying a penny more than not being able to buy apples at all.

      Or, an individual rationed buyer will offer a penny more, because then all sellers will want to sell to him rather than to other buyers, so he won't be rationed.

      Same thing in reverse if P > P* and so some sellers are rationed.

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    17. Excellent. That's what I thought you would say. You can slip that by an undergraduate, but it won't work with another economist. In this partial equilibrium competitive model, the consumers maximize treating P as given, and they act under the belief that they can buy as much as they want at price P, subject to their budget constraints. Similarly, the firms think they can sell as much as they like at price P. No economic agent in that model sets prices, and we have not described how the economic agents in the model will deal with being rationed, for example if a consumer tries to purchase the goods he wants at price P and can't find a seller to supply the goods. So, the story you are telling is just a story - it's outside the model, and not part of the competitive equilibrium paradigm.

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    18. Steve: of course it's just a story. So is any model. We tell some stories in words, and we tell other stories in math. And to my mind some sort of story like that is an integral part of the competitive model. And it's a good story.

      They maximise taking P as given, assuming they can buy or sell as much as they want. Until they can't, because P /= P*. And that's when they offer or demand a different price.

      To my mind, the story I have just told is better than the story of a Walrasian auctioneer, who has some very weird objective function, and won't allow anyone to trade until he has discovered P*. But that is at least a story.

      I can also re-tell my story in terms of monopolistically competitive price-setting firms, if you like (but they don't strictly have supply curves).

      You don't have any story at all! My story, based as it is on individual maximising behaviour, is better than your non-story!

      *Who* sets the price in your model? What is that individual trying to maximise? Or are prices set by some divine entity, who wishes to maximise the satisfaction of Euler equations?

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    19. "Steve: of course it's just a story. So is any model."

      Exactly. The whole story should be in the model. I can always say some words about the forces that are at work in the model, to help people understand it. Your story is not that. It's a story based on some other model, so it doesn't help people understand what is going on in the model under consideration.

      The Minnesota people are/were very good at this. There are rules of the game. You need a model to beat a model. Your discussion of the science of what you are doing is confined to what is going on in the model at hand. etc.

      "*Who* sets the price in your model? What is that individual trying to maximise? Or are prices set by some divine entity, who wishes to maximise the satisfaction of Euler equations?"

      Those are questions that we could ask of any competitive equilibrium model, which of course accounts for a large fraction of work in economics. One answer to the question is that, if you allow some economic agents to set the prices, then the answers typically don't change much, if at all. So why bother with the complications of price setting? In some contexts - search for example - you have to get serious about bargaining and pricing.

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    20. Egad, Nick Rowe really is a low-ranked monkey, isn't he? Nick, wherever you got your PhD owes you an apology, they clearly didn't teach you anything.

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    21. Steve: " One answer to the question is that, if you allow some economic agents to set the prices, then the answers typically don't change much, if at all. So why bother with the complications of price setting?"

      Because in your model here, the answers could change a lot, under any reasonable story of agents setting prices.

      For example, suppose that inflation is too low to satisfy your Euler equation (1). That will (usually) mean there is excess supply of output in the current period. Or, in a world of monopolistically competitive firms, each firm is selling where MR > MC. So the individual firm would like to cut its price relative to other firms' prices, in order to increase sales.

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    22. BTW: let's start in equilibrium, then suppose the central bank raises the nominal interest rate. What happens to inflation?

      I think the answer to that question depends on agents' answer to the question: "Why did the central bank do that?"

      They have new information about the central bank's preferences or beliefs, and how agents will respond will depend on how they update their own beliefs about the central bank's preferences and beliefs.

      That is how I tried to handle this question in my most recent post.

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  2. Fine response, clearly and precisely presented, making the entire argument worthwhile.

    anne

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  3. Comments critical of Williamson's tone have in fact been deleted. Well done, Steve! That's the way to answer your critics!

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    1. I delete comments where people cross the line between what is constructive and what is personal/abusive.

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    2. None of the comments posted last night did that.

      I find the smarter-than-you attitude on display here, especially in your first paragraph, to be off-putting and entirely misplaced. That's neither personal nor abusive.

      You also deleted a question as to why we should prefer your model to Krugman's explanation for the lack of deflation -- which you claim we should -- given that Krugman cites to a empirically established effect (wage rigidity) and your model is purely speculative. If you think that's personal, then I think you need to revisit your understanding of that word.

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    3. "I find the smarter-than-you attitude on display here, especially in your first paragraph, to be off-putting and entirely misplaced."

      For me, that's getting personal. You might as well have said: "Who do you think you are , Mr. Smarty Pants?"

      Basically, this is my blog, and you have to live by my rules. Suck it up.

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    4. Of course I have to live by your rules. But I don't think your rules paint a flattering self-portrait.

      For instance, I think you're making up the "who you do you think you are" part? Why, I don't know. I'm not suggesting that you shouldn't have an opinion. It's just that there's a difference between bowing to the supposed intellectual authority of Paul Krugman (you're right not to), and talking to him (and many others) as if he were a fool.

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    5. "Of course I have to live by your rules. But I don't think your rules paint a flattering self-portrait."

      See, there you go again. Don't be so nasty.

      It's not calling someone a fool to say he or she is confused. In fact, it could be my fault that they're confused. I think you're being overly sensitive.

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    6. Yet somehow "Egad, Nick Rowe really is a low-ranked monkey, isn't he? Nick, wherever you got your PhD owes you an apology, they clearly didn't teach you anything." remains preserved for Internet posterity...

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  4. CA wrote:

    My understanding is that the liquidity premium is the difference between the price of the bond that would prevail if it only served as a tool for transforming current consumption to future consumption (e.g. if the rate of interest were equal to the rate of time preference) and the one that prevails when the bond can, in addition, be used as a medium of exchange.


    There is no reason to think that "premium" depends at all on the scarcity of the bond. If money is freely available, then there is no shortage of liquidity. Why would you pay for it in the price of a bond? Surely the amount you would pay wouldn't depend on the quantity of those bonds -- again, since liquidity is freely available.

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    1. Yes, money is freely available, but when the nominal interest rate is positive, the agents in the model don't want to use money when they can use bonds, as they get a better deal with bonds. Your intuition is correct in the liquidity trap, where money and bonds are used to buy the "bond goods."

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    2. If so, what does it mean for a bond to have a liquidity premium in the liquidity trap?

      Let me put it this way. When you say my intuition is correct in the liquidity trap, aren't you saying that bond scarcity doesn't have an effect? And doesn't that undercut the entire argument in the liquidity trap environment?

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    3. Well, I guess you're not as correct as I thought. All of the assets are collectively scarce in the liquidity trap. The liquidity premia are the same on both assets. With a positive nominal interest rate, the liquidity premium on money is higher.

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    4. Steve, yes, this is exactly what I had in mind. And monetary policy is ineffective because swaps between the two assets does not address the problem, which is the limited supply of the two combined.

      By the way, when I started visiting your blog. reading something like this would have had me just as confused as anonymous. I feel I have learned quite a bit from following. It is like attending a top program even though I didn't have the chance to do so the first time. For that, thanks!

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    5. No problem. At least one satisfied customer, so I'm making progress.

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  5. Williamson wrote:

    "The model, in fact, does not allow risky assets to be used as collateral."

    You can add that, and get the same things. See my AER paper.


    Not true, unless you have factored in endogenous price changes of those risky assets, which I do not see in that AER piece.

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    1. I guess that depends on what you mean by risky assets. In the AER paper, there's a section where there is lending to entrepreneurs to finance investment projects. Those projects are risky. But the bank diversifies across projects, and so the idiosyncratic risk is diversified away. But there is costly state verification (roughly bankruptcy costs), so there are default premia, which get priced in. This actually makes the idiosyncratic risk matter. Basically, the more risk there is, the costlier lending is, and the higher is the default premium for a given borrower - there's an increase in interest rate spreads. Further, the real interest rate on safe debt falls. Kind of interesting, don't you think?

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    2. I just realized I was looking at your working paper, not the AER piece. I will have to read the AER paper at some point, I guess

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  6. Hi Stephen,

    You provided a link to a Brad Delong post regarding the disequilibrium foundations of equilibrium economics (to borrow the title of Franklin Fisher’s book), but I don’t think you address either Delong’s post or Franklin Fisher’s account of the difficulties involved in showing how the behavior of agents in out-of-equilibrium states eventually results in an equilibrium.

    Here’s Delong’s citation from Fisher:

    “Analysis generally proceeds by finding positions of rational expectations equilibrium if they exist. At all other points, agents in the model will have arbitrage opportunities…. The possibility of such arbitrage (plus the assumption that agents are smart enough to take advantage of it) is enough to show that points that are not rational expectations equilibria cannot be points at which the system remains…. Yet this, by itself, is not enough to justify analyzing… as though such equilibria were all that mattered…. The fact that arbitrage will drive the system away from points that are not rational expectations equilibria does not mean that arbitrage will force the system to converge to points that are rational expectations equilibria, the latter proposition is one of stability and it requires a separate proof, Without such a proof–and, indeed, without a proof that such convergence is relatively rapid–there is no foundation for the practice of analyzing only the equilibrium points…"

    I think Fisher's claims bear on several points debated above, e.g., "There are optimizing agents in the model, they optimize, and in equilibrium that's what happens." What do you think?

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    1. See my reply to Paul Krugman, which is the latest post. This is basically a criticism of all competitive equilibrium models, and does not have anything in particular to do with my model. And much of economics is competitive equilibrium, so if this is a problem for me, it's a problem for most of the profession. The textbooks are full of it.

      Generally, the stories about convergence to competitive equilibrium - the Walrasian auctioneer, learning - are indeed just stories. Those stories come from outside the model. Competitive equilibrium models are just that. There is no meaning to "out of equilibrium behavior" for example, as that doesn't happen in the model.

      However, if we care about price setting, learning, rationing, etc., economists do have ways of building those things into models. Search theory works nicely, for example.

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  7. I'm a little confused and I'm sorry in advance if this is a stupid question.

    In your liquidity trap notes, in the model with the liquidity trap you have inflation = 0 (equation 21). Is that correct? That would imply that marginal utility is zero. Ok I guess. But then you have the real return on government debt as (1/inflation)-1. Wouldn't that be infinite? And then that has to be *less than* (1/beta)-1.

    Is this a typo or am I missing something?

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  8. Looking at it again, I think it's just that "=0" shouldn't be in there.

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  9. "This is to capture the idea that government debt and other safe assets are useful in financial exchange and as collateral. In an equilibrium in which the value of the consolidated government debt is sufficiently small, asset-in-advance constraints bind, and the low quantity of consolidated government debt tends to make consumption and output low, produces an inefficiency wedge, increases the liquidity premium on government debt, and reduces the real interest rate."

    I don't know how accessible you want to make your explanations here to non-macroeconomists (although you'd probably say Krugman is a non-macroeconomist), but I'll give this a try:

    It seems like you're saying that there's a shock that makes the perceived quality of bonds go down. So now there's less collateral in the economy, and so less borrowing and economic activity.

    Your solution is to add more high quality capital that can be used as collateral in the form of government bonds.

    But isn't actual cash the ultimate collateral? If the Fed, in a QE, buys a bond that's worth $X for $X cash, can’t the $X cash do anything that the bond could do? With the bond you could borrow some percent of the $X in cash. With the cash you actually have $X, the full $X. How is the bond superior to a cash equivalent in motivating a firm or individual to spend or invest?

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    1. Richard,

      The last paragraph in your comment is the standard motivation for an open market operation - swapping reserves for bonds increases liquidity. But what happens at the zero lower bound? In that case, bonds and money are equally liquid, and it doesn't matter. But the Fed says: I know of something less liquid than reserves and short Treasuries - it's long Treasuries. So if the Fed swaps reserves for long Treasuries, the Fed has increased liquidity.

      So, this gives some content to that story. What does it mean for long Treasuries to be less liquid? They're worse collateral.

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  10. I'm hardly an expert at this stuff (although I do understand most of it), but even I can tell you that either not bothering to actually read Krugman's entire argument before you respond to it, not bothering to actually understand it, or blatantly misrepresenting it, and then refuting things he didn't actually say, is not actually going to win you a lot of points.

    Also, I wonder, are you actually refuting the existence of nominal downward wage rigidity, or are you just arguing that it is irrelevant? Because we now have a LOT of evidence as to its existence, and its strength, which you seem to simply ignore.

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