## Tuesday, June 10, 2014

### How does a liquidity trap work?

I've been getting in arguments with market monetarists (in particular Scott Sumner and Mark Sadowski) about the liquidity trap lately. See e.g. comments here [1] and here [2]. I don't think they understand the liquidity trap model. Maybe they just discount the model assumptions that disagree with their assumptions and are therefore effectively talking about a different model. It's possible it's my fault because I don't understand the liquidity trap argument or the monetarist argument (or both). So I decided to make some nice pictures and put forward what I think the Keynesian and the monetarist views of the liquidity trap are.

Here is the basic picture, borrowing from Figure 1 (on page 9) Figure 2 on page 13 (aka p149) [H/T Mark Sadowski] of Paul Krugman's 1998 Brookings paper (we start before the recession hits that causes the liquidity trap; Krugman starts from an economy in a liquidity trap). The dashed curve represents the Hicksian IS curve in the pre-liquidity trap picture with the black point representing the equilibrium interest rate and output (the money market equilibria at a given output are given by the gray vertical line). Suddenly a shock hits, moving the output to the left and now the set of money market equilibria are given by the red line (which would select the red point on the dashed IS curve). However, the shock also drives the IS curve to the blue curve. The equilibrium solution Z is now below the zero lower bound (ZLB), and the region where the IS curve is < 0 is shaded in blue.

Note that it is the fact that the equilibrium point Z is below the ZLB that indicates the liquidity trap, not the position of the current state of the economy in the light blue region (the red or black dots). I think this is a major source of misunderstanding between the two sides. It doesn't matter if a country has positive interest rates ... it can still be in a liquidity trap.

The first question we need to ask is: Where does the red dot go when the IS curve shifts?

The Keynesian answer: nowhere, necessarily. The IS and money markets have become disconnected and their intersection no longer determines the equilibrium. The central bank may try to move the red dot to the ZLB (zero interest rate policy, ZIRP) straight down along the red line from point #1 to point #2.

The monetarist answer? I'm not sure. The red dot may stay where it is (#1), but some evidence indicates that market monetarists think the red dot moves to the zero lower bound at point #2 or that the money curve shifts to the left, moving the equilibrium to point #3 (see figure on the left above). The latter is more consistent with the market monetarist belief that the central bank causes the recession through monetary policy.

Scott Sumner and Mark Sadowski point out that the ECB has positive interest rates, which means -- to them at least -- the EU isn't even at the ZLB. This may be evidence that the point stays at point #1 when the shock hits (like the Keynesian answer), or it may be evidence that the money curve shifts even farther to the left and the ECB is at equilibrium #4 in the figure on the right above (or even all the way over to point #5 that keeps the interest rate constant).

Only points #1, #2 and #3 could be characterized as an economy in a liquidity trap (the last one, only marginally). However, only points #1 and #2 are consistent with the modern description of the liquidity trap. Krugman states that moving to #2 doesn't hurt, and if the fall in the IS curve is slow, the equilibrium point will follow the curve down until it hits point #2. My interpretation is that Krugman believes point #1 is the EU and point #2 is the US.

The second question we need to ask is: Where does the red dot go when the central bank raises interest rates in a liquidity trap? We'll say the economy starts at point #2, which is Krugman's point #3 in Figure 1  2 in his 1998 paper (see the figure below), showing an economy in a liquidity trap.

The Keynesian answer: the economy moves to point #6 in the diagram above, or possibly the point next to it. The equilibrium point is free to move up or down (at least, down to the ZLB). To leading order, the IS and LM markets are disconnected, the central bank has no traction and the effect of interest rate policy has no impact on output.  Raising rates does send a contractionary signal, which can cause deflation/disinflation through expectations (e.g. the ECB raising rates in 2011) reducing output. Raising rates also will cause e.g. budget constrained EU member nations to reduce government spending and put the savings toward increased debt service. The central bank could send an expansionary signal but this is hard to do (it is hard to promise the inflation will stick around). Effectively, the central bank cannot move the red line (output) left or right.

The monetarist answer: the economy moves to point #7. The economy is no longer in a liquidity trap or at the ZLB. By assumption, the central bank can generally offset changes in output through monetary policy (moving the red line to the left or right), effectively taking the blue curve to be the dashed blue curve in the ZLB region (blue shaded region). This means that monetary policy can offset fiscal policy through its effect on output in the AD/AS model. This is the diagram monetarists say describes the ECB raising rates in 2011. (Note that point #7 here is Krugman's point #1 in Figure 1 2 in his 1998 paper, which shows an economy that's not in a liquidity trap.)

The third question we need to ask is: How do we get back to pre-recession output?

The Keynesian answer: fiscal stimulus is the only thing that will move us from point #2 to point #8 in the diagram above. In terms of monetary policy, we're stuck at point #2.

The monetarist answer: if the central bank targets the output level given by point #8 (moving the red line to the right), we can move along the dashed blue curve to point #8. Monetary policy effectively selects the level of output ... by assumption.

The fourth and final question we need to ask is: Which answers are right?

This is the Keynesian/Hicksian/Krugmanian liquidity trap model, so I'd defer to those answers for how a liquidity trap works. But I think I've captured where different model assumptions enter. Because macro data is uninformative, the argument between both sides tends to take the form of "obviously the (Keynesian/monetarist) model assumptions are correct" and "such and such random piece of (monetarist/Keynesian) model confirming data show that the (Keynesian/monetarist) model is wrong". Neither side cedes that model assumptions on the other side could be correct, nor do many of the blog posts out there look at all the data together. The two sides are talking past each other. They have different models and assumptions and each side doesn't believe the other one.

Now I believe the evidence is strongly in favor of the liquidity trap model, at least for the US, Japan and the EU. The information transfer model allows both explanations to exist, but selects which one based on the empirical data. It favors the liquidity trap view in the case of Japan, the US and the EU. It favors the monetarist view for countries like Canada, Australia and Sweden. In order to do this, it looks at all of the data (price level, NGDP, monetary base, and interest rates) together.

Now maybe the information transfer model is incorrect, but at least it doesn't assume the result.

1. Jason, I enjoyed your interchange with talldave2.

2. Jason, in one of talldave2's comments to you, he wrote this:

"I don’t know the ECB or BOJ notes well enough to say much there, but it doesn’t really matter, because again, trivial to prove their missing low is a choice — is there nothing they can do to miss high if they choose to? Are there no assets in the world left to purchase? Do they no longer own printing presses?"

Which got me thinking about something you wrote once, which was that a bout of hyperinflation could free a country like Japan from an information trap (liquidity trap?). If we take talldave2 at his word here and assume the CB would stop at nothing to raise inflation (buying up as much of everything as there was to buy as possible), do you estimate that this could be one way to induce the bout of hyperinflation that you referred to before?

When you brought up hyperinflation as an escape mechanism from the information/liquidity trap before, how were you imagining that could be accomplished? Since dP/dM ~= 0, how do you get to (hyper)inflation from there?

Here's talldave2's comment:

http://thefaintofheart.wordpress.com/2014/06/07/what-simon-wren-lewis-thinks-he-knows-is-not-true/#comment-14371

1. I especially loved this part:

Jason, I love this:

"P = inflation is x%
Q = CB is targeting x% inflation
Axiom P→Q (assume a CB can always get x% inflation)
Observe P (inflation is x%)
Therefore Q (CB is targeting x% inflation)

It’s totally logically consistent (and even consistent with empirical data), but it doesn’t explain anything. It takes the condition of the world as it is and says that the world is that way because it has to be that way."

I'd like to see more people point out this kind of thing on econ blogs. talldave2 responds by saying that you should just look at the Fed minutes to see that they were more concerned with inflation than deflation. He goes on to say that he doesn't know about the BoJ minutes, but it should be easy to "prove" they did the same thing, and that furthermore you should always look at evidence such as the CB minutes before going on to build empirical models. Specifically he writes this:

"Never use an empirical model when you can just ask a person why they did something."

A couple of things occur to me.

1. Occasionally people at the Fed do answer questions from people like me (nobodies essentially). For example David Andolfatto or maybe even Steven Williamson (I tried the former, with some success, but not the latter). They may not be making these decisions, and they may not answer that pointed of a question even if they were, but they are literally people to ask (rather than minutes to read).

2. Do you think it's fair to suggest that talldave2 (or someone that shares his views on this) should really produce a model that takes CB minutes (and other data) as inputs, and produces as an output the inflation rate? Maybe I'm not being fair, or looking at that the right way, but what he's saying would be a lot more concrete if there was a model that did this, especially one that pumps out quantitative "predictions" (I put it in quotes since it may always be the case that the inflation figures are already known by the time the minutes are made public) rather than just qualitative statements. Do you think what I'm trying to say here has some value, and if so how would you rephrase it to make more sense? :D

2. Jason, can you expand on what you mean by this:

"Maybe these models are wrong, but they are stark evidence that P→Q is a model assumption."

3. Hi Tom,

Regarding the hyperinflation, yes, that is a way that a central bank could inflate (and exit the liquidity trap -- and that seems like what happened after WWII), but that always produces accelerating inflation (at least in the information transfer model). My argument with talldave2 was that central bank can't choose a fixed inflation rate to target. If it tries to target an inflation rate, you get the liquidity trap model -- basically, if NGDP and MB are "endogenous", you eventually get the liquidity trap. Hyperinflation takes MB as exogenous and NGDP as endogenous. If it tries hyperinflation, it doesn't get to choose the initial inflation rate and the rate changes (i.e. accelerates). The Fed would get some inflation rate that is a priori unknown (at least in the information transfer model -- it is possible the new parameters of the hyperinflating model would be related to the previous fitted parameters, but there really isn't a reason for that to be always true). The hyperinflation would produce i = 5% in year 1, then i = 10% in year 2, and i = 20% in year 3, etc.

Regarding the empirical models, it seems talldave2's model is unassailable through empirical analysis. It may be possible for e.g. Google to build a database of Fed minutes and find some fixed relationship between words they use and the outcome. However, as talldave2 points out, that could change once you know the model. So a central bank can always produce x% inflation and if you try to empirically test this, the relationship will change and empirical models can't capture it. [What is that sarcasm mark again? ... ؟]

Regarding P→Q (if inflation is x, then the central bank is targeting x), what I was saying there is that models exist that do not assume P→Q and also where P→Q actually fails to be true. Therefore P→Q cannot be universal axiom -- it must come from an empirical regularity, if it is true at all. [Also P→Q means that the US inflation target has fallen from 5% in 1985 to about 1.5% today along a relatively smooth path ... I'm sure the Fed minutes from 1985 say targets of 5%, 1990 say targets of 4%, the late 90s say 3% and the 2000s say 2%]

4. Jason, the ؟ mark is totally new to me. Thanks... that was interesting.
Regarding:

"[Also P→Q means that the US inflation target has fallen from 5% in 1985 to about 1.5% today along a relatively smooth path ... I'm sure the Fed minutes from 1985 say targets of 5%, 1990 say targets of 4%, the late 90s say 3% and the 2000s say 2%]"

Missing the sarcasm mark on that one?

Again, back to this:

"but they are stark evidence that P→Q is a model assumption.""

Are you saying the existence of the two other types of models you mention, namely:

1) Models that do not assume P→Q

2) Models in which P→Q fails to be true

are stark evidence that talldave2's model does assume P→Q? Sorry to be so dense on this.

I think I see what you're saying in the last paragraph above, although "empirical regularity" is a new one for me. I'll Google it.

5. Yes, basically. What I mean is the existence of sensible models where the central bank can't target any particular inflation rate is evidence that the statement "the central bank can target any inflation rate" is not necessarily always true and that talldave2 is assuming it.

6. Regarding the empirical models, it seems talldave2's model is unassailable through empirical analysis.

It's not only possible but trivially easy: find me a single example of a CB trying and failing to inflate. Sorry, CBs deliberately missing their target low by a little bit don't count, no one is claiming they're capable of arbitrary precision, and the Fed itself admits they miss low on purpose.

My argument with talldave2 was that central bank can't choose a fixed inflation rate to target. If it tries to target an inflation rate, you get the liquidity trap model -- basically, if NGDP and MB are "endogenous", you eventually get the liquidity trap. Hyperinflation takes MB as exogenous and NGDP as endogenous. If it tries hyperinflation, it doesn't get to choose the initial inflation rate and the rate changes (i.e. accelerates). The Fed would get some inflation rate that is a priori unknown (at least in the information transfer model -- it is possible the new parameters of the hyperinflating model would be related to the previous fitted parameters, but there really isn't a reason for that to be always true). The hyperinflation would produce i = 5% in year 1, then i = 10% in year 2, and i = 20% in year 3, etc.

This seems like a very strange argument to make. During the Great Inflation, as is well known, the Fed tried to target employment, and mostly ignored inflation. The result was a lot of inflation, but certainly not hyperinflation. Eventually under Volcker the Fed decided to target inflation and forced a recession to break inflation. Remember, the Fed has always had a dual mandate, so at least in theory it is always targeting both inflation and employment, though it tends towards one or the other.

What I mean is the existence of sensible models where the central bank can't target any particular inflation rate is evidence that the statement "the central bank can target any inflation rate" is not necessarily always true and that talldave2 is assuming it.

Those models aren't sensible unless they can explain why the Fed is unable to print more money. If you have a model that involves arresting the Fed governors, that might work :)

7. "[Also P→Q means that the US inflation target has fallen from 5% in 1985 to about 1.5% today along a relatively smooth path ... I'm sure the Fed minutes from 1985 say targets of 5%, 1990 say targets of 4%, the late 90s say 3% and the 2000s say 2%]"

Again, this is a very strange reading of history or my argument, I'm not sure which. Why did Volcker have to raise rates so high that it induced recession to break inflation? Because it was the only way to make the target credible -- it was about changing expectations, in other words. Expectations have a lot of inertia, then and now. Obviously the Fed cannot wave a magic wand and achieve any inflation target it desires overnight with arbitrary accuracy, but just as obviously there is always some action they can take (raising rates, printing money) that will have some effect in the desired direction.

8. Maybe I'm making this too hard. Let's go back to my irrefutable example:

Suppose the Fed wants minimum 7% inflation over the next 12 months. You say this is not possible, the Fed cannot inflate right now. I say the Fed can start sending money to people and double (or triple, or 10x if you like) until they get the inflation they want. Let's further assume they don't care much if they overshoot.

How many billions or trillions or quadrillions of dollars do you suppose the Fed can send out without creating inflation?

9. You may have issues with some the arguments above because they involve the information transfer model. In that model, the maximum amount of inflation a central bank can generate falls as the base gets larger relative to the economy. It does however allow ever-increasing (accelerating) inflation if the central bank ignores the economy. There are no stable paths of inflation in the model.

In this model, if the Fed started printing money, either deflation or hyperinflation would result. The former happens if the Fed conducts the policy (money printing) through open market operations; the latter happens if the Fed gives the money away.

In the former scenario, widespread deflation would cause the economy to collapse.

In the latter scenario, the Fed could have 7% inflation in the first month but could have upwards of 50% inflation by the end of the 12 months.

That's in that model, though.

10. Jason, you write:

"In this model, if the Fed started printing money, either deflation or hyperinflation would result."

What would determine whether deflation or inflation would result? Are you saying that there's not a unique solution to the model in some circumstances?

11. What determines the result is whether the base is "endogenous" or "exogenous" in the sense of this post

http://informationtransfereconomics.blogspot.com/2013/10/exogenous-and-endogenous.html

Endogenous would be something like the Fed putting currency in the market via open market operations (it's deflationary when the base is large, inflationary when it is small). Exogenous would be something like the Treasury printing currency to pay government contractors or mailing it to people (it results in accelerating inflation).

The mathematics of it are pretty straightforward -- I think I have the interpretation of it right, but it's not as cut and dried.

Now, given data, it may not be as easy to back out what is going on. For example, It is hard to say when Argentina's hyperinflation actually started:

http://informationtransfereconomics.blogspot.com/2014/01/rich-countries-poor-countries-japan-and.html

12. OMOs are only deflationary if the Fed is selling assets. See Nick Rowe's "rising house prices are indeed caused by building too many houses" post.

13. Jason, thanks. Also you answered another of my questions:

"Endogenous would be something like the Fed putting currency in the market via open market operations (it's deflationary when the base is large, inflationary when it is small). "

I wasn't sure how you were using the terms endogenous and exogenous, so that clears that up. I don't believe that's how everyone uses them, but not matter.

Sproul and Sumner have continued their discussion which I think touched on this very issue, both in the comments to Scott's response to Sproul, in the in the comments to Glasner's latest. I think Scott was misunderstanding something about Sproul's backing theory, and that had to do with "reflux channels." Upshot: Sumner and Sproul seem to agree that OMOs are inflationary when all reflux channels have been cut off (meaning, a channel by which currency can be redeemed for something more valuable). Well, that's the takeaway I grasped anyway, but take a look for yourself:

http://uneasymoney.com/2014/06/09/the-backing-theory-of-money-v-the-quantity-theory-of-money/#comment-160201

And Mike's comment right below. Then at the end of Sumner's old post on this.

14. re: exogenous vs endogenous: I think Sumner would say that if the CB targets an MB (and by that I mean the usual definition of MB, not just the currency component) it doesn't matter whether it does so by just writing people checks, or by performing OMPs: those are both examples of an exogenously targeted MB level (especially if the target is set arbitrarily, and is not part of a bigger plan to target the inflation rate or the interest rate or something). Of course I'm assuming by my language here that the MB target is > the current MB level, but that's not a necessary assumption.

3. "Note that it is the fact that the equilibrium point Z is below the ZLB that indicates the liquidity trap, not the position of the current state of the economy in the light blue region (the red or black dots). I think this is a major source of misunderstanding between the two sides. It doesn't matter if a country has positive interest rates ... it can still be in a liquidity trap."

I could not disagree more. This has absolutely nothing to do with the disagreement.

1. Great -- that clears that up. I guess it was my misunderstanding.

4. Hi Jason, enjoyed our discussion :)

1 and 2 are basically okay I think. For 3, I think this may be asking the wrong question. For one thing, output is already higher than in 2008. A better question might be "how do we maximize real output?" The monetarist answer is NGDPLT, the Keynesian answer is that only fiscal expansion can help when we're at ZLB.

The monetarist answer: if the central bank targets the output level given by point #8 (moving the red line to the right), we can move along the dashed blue curve to point #8. Monetary policy effectively selects the level of output ... by assumption.

Monetary policy that targets NGDP can effectively select the level of NGDP, but that's not an assumption, that's been empirically proven by basically every CB that has ever tried to inflate. They can't do so with arbitrary precision, but they can certainly inflate, and thus effectively set NGDP. They have printing presses, there are assets that can be bought, failing all else they can just send money to people.

The monetarist argument is that in 2008-9, the Fed should have targeted NGDP rather than allowing the largest NGDP fall since TGD. That would have alleviated a lot of pain, and produced more employment and output.

Unlike the Austrians, monetarism don't really oppose fiscal expansion per se. If you want to move from a Hong Kong style government of ~25% of GDP to a pre-1990 Swedish economy of ~70% GDP, or vice versa, monetarism doesn't really express any strong preference either way. It just says that whatever the fiscal side does, the economy will be better served by an NGDP target than a strict inflation target, especially during recessions.

1. Hi Dave, I enjoyed it too :)

Yes, output is higher than in 2008 -- that is one of the difficulties with a quasi-static analysis. The pictures should all be considered to happen around the end of 2008 in the US (except for the rising interest rates scenario).

NGDPLT is exactly the statement the central bank can choose the location of the red line -- the line is defined by y = k M/p, i.e. NGDP = p y = k M. So I think we're saying the same thing there. The central bank can set the red line at point #8.

2. I guess the fourth question is is where it gets interesting :)

So, who's right? Here are the two major flaws in the LT model:

"The central bank could send an expansionary signal but this is hard to do (it is hard to promise the inflation will stick around)" There's no explanation of why the CB can't change their long-term targets. Why is this "hard?" They still own printing presses. There are still assets to purchase. Markets still respond to CB expectations. No CB has ever tried to inflate and failed. It may be politically difficult for a CB to raise inflation permanently, but never economically or mechanically.

Also, I don't know if LT proponents have an explanation for why first Japan, and now the US and EU have fallen into ZLB, but MM does -- one that goes back many decades to "old monetarists" like Fisher and later Friedman. They predicted that a low-inflation-target regime like the Volcker/Greenspan/Bernanke policy would eventually (over decades) result in low nominal rates as the expectations for inflation gradually fell. MM's answer is to stop doing what sent us into ZLB, and target NGDP instead; problem solved. I don't know what the LT model's endgame looks like, does this model expect interest rates to rise eventually, and return to normal economic rules? If so, why? Fiscal expansion can't continue forever, except under some extremely odd assumptions like those found in MMT.

5. "Here is the basic picture, borrowing from Figure 1 (on page 9) of Paul Krugman's 1998 Brookings paper (we start before the recession hits that causes the liquidity trap; Krugman starts from an economy in a liquidity trap)."

Figure 9 in Krugman's paper is drawn in interest rate-price level space. Consequently it has little directly to do with the IS/LM Model which is drawn in interest rate-real output space.

LM curves are typically drawn upward sloping and there is a more recent variant known as IS-MP where the LM curve is replaced by a horizontal MP (monetary policy) curve.

http://eml.berkeley.edu/~dromer/papers/JEP_Spring00.pdf

Krugman is a recent convert to this model and both versions were taught to me in graduate school.

Note that in the IS/MP version there is absolutely no chance of any indeterminancy since the central bank is targeting an interest rate and the MP curve is above zero interest rates (i) at all levels of real output (y). Since the IS curve is downward sloping, lowering the MP curve *must* raise the level of real output. The only constraint to the central bank's ability to raise the level of real output is thus the ZLB.

Do I believe this? No, but at the very least if *you* are going to model this with IS/LM or IS/MP Model, at least draw the LM or MP curve in a more conventional manner.

There are other alternatives to the conventional IS/LM Model worth considering, and Nick Rowe has shown these on his blog. But for the moment I would like to keep this as simple as possible.

1. Hi Mark,

Whoops. I meant Figure 2 on page 13 (aka page 149). I'll change that. (It is almost the exact same diagram as Figure 1 except output is the x-axis -- I apparently messed up when I went to write down the reference.)

Apart from that, the diagram is consistent with Krugman's paper.

The vertical curve is labeled as the MM curve in the paper representing the cash in advance constraint, Y = M/P, and shifts in it are shifts in the money supply. I didn't want to get MM confused with market monetarist, and so I just referred to it as the money curve (or the set of money market equilibria at different interest rates associated with a given output). Additionally, that formulation has a direct connection with the quantity theory of money (i.e. the MM curve is exactly where you set it with PY = M so you can see what boosting M does ... or NGDP targeting).

You could add the MP curve -- it intersects with the vertical "MM" curve at the same point on the IS curve the MM curve intersects with it for an economy in equilibrium. I was hoping to keep it simple and have a direct connection to Krugman's 1998 paper -- where he only shows the MM curve and the IS curve.

2. OK. At least we're on the same page now (literally).

But notice that the IS curve is downward sloping. So to maximize real output you want to shift the MM curve to the right at least to the point where the IS curve crosses the horizontal axis. If interest rates are above zero then the MM curve is to the left of that point, and if the MM curve is to the right of that point *interest rates will be zero* (see Krugman page 146).

In short, positive interest rates are always less than optimal in the modern conceptualization of the "liquidity trap".

3. I think I just committed a similar error as you did. The correct page number is 149.

4. I see what you are saying and I agree that if you come in from the left starting at positive interest rates (say point #7 in the second to last diagram which is Krugman's point 1 in his diagram), you go to zero at point #3 above (the zero crossing of the IS curve). That is exactly what Krugman says.

In the argument Krugman says you can't get to point #2 from the left by increasing the money supply (my point #2 is his point 3, see p146). However, you can find yourself at point #2. In that case you can raise interest rates and it should just move you up and down the MM curve (to e.g. point #6). That means interest rates are pretty much irrelevant.

One way of looking at this is to assume the IS curve exists to the right of the zero crossing but is replaced with a segment at zero interest rate. However, I think Krugman is trying to say that the IS curve doesn't exist (it's solutions are nonsensical) to the right of the zero crossing.

That leaves undetermined what happens if you were to raise interest rates from point #2 or lower them from point #1 in the diagrams above.

I believe you are saying that the equilibrium slides to the left and up the IS curve to point #7. And that seems to make sense, but it's outside the underlying model.

I put together these two pictures:

In the second one, sure, you follow the blue line. In the other, I'm not sure what happens.

5. *The level of interest is determined entirely by the IS curve in this particular model*.

The IS curve does not exist below the horizontal axis. One can shift MM to the right beyond the point at which the IS curve intersects the horizontal axis but it becomes irrelevant. Thus the interest-real output equilibrium is at point #2 in Krugman's diagram.

As I said before, positive interest rates are always less than optimal in the modern conceptualization of the "liquidity trap".

6. Hi Mark,

I think I understand your take and completely agree that in that view, positive interest rates are not optimal and that monetary offset occurs.

The point of disagreement (by which I mean substantive -- we're using different models) is that to the right of the IS intersection with the axis, there is no connection between interest rates and output.

Here's my personal take (i.e. not playing devil's advocate with the IS-LM model) with the information transfer model:

http://informationtransfereconomics.blogspot.com/2014/06/krugman-keynes-and-liquidity-trap.html

6. This comment has been removed by the author.

Comments are welcome. Please see the Moderation and comment policy.

Also, try to avoid the use of dollar signs as they interfere with my setup of mathjax. I left it set up that way because I think this is funny for an economics blog. You can use € or £ instead.