Is this a liquidity trap?

 

That's not a picture of the Canadian economy. But it is, I think, a good picture of the US economy right now. And maybe Japan, and maybe parts of Europe too.

Let me try to explain it.

0. Just set aside the distinction between real and nominal interest rates. My picture ignores that distinction, and so implicitly assumes expected inflation is constant. There's an interesting and important debate on whether central banks could escape a liquidity trap by increasing expected inflation. But that's not the topic of this post.

1. The economy is currently at the "we are here" point. The rate of interest (on safe short assets) is currently 0%. (I couldn't draw it exactly at 0% without messing up the picture, but ignore that). Real income is currently less than Y*, which you can think of as "full-employment income", "potential output", "NAIRU output", the "natural level of income", or "that level of income consistent with the economy being on its Long Run Aggregate Supply curve or Long Run Phillips Curve".

2. But the actual rate of interest (0%) is less than the "natural rate of interest" r*. That's what's different about my picture. In normal pictures of a liquidity trap, the IS curve is drawn sloping down, so the interest rate r* at which the IS curve cuts the "full-employment income" line is less than the actual rate if the economy is at less than full-employment income. The normal picture of a Zero Lower Bound liquidity trap has a negative natural rate. Mine has a positive natural rate.

3. Why does my IS curve slope up? It is not because I think that a higher interest rate would increase demand for newly-produced goods. Rather, it is because I think that a sustained increase in demand for goods would have such a strong self-reinforcing effect on desired investment and consumption that interest rates would need to rise to keep output demanded equal to output. The marginal propensity to invest plus the marginal propensity to consume exceeds one, in other words. Take a normal Old Keynesian IS curve, and assume mpc+mpi>1, and it will slope up.  I explain this more in an earlier post.

4. I have drawn two LM curves. The horizontal LM curve is what is normally drawn in pictures of a liquidity trap. It is also the LM curve that is normally drawn by economists who think of monetary policy as setting a nominal interest rate. So I need to explain my vertical LM curve.

5. Take the Bank of Canada for example. In the very short run, you might describe the Bank of Canada's monetary policy as setting a nominal rate of interest. But that very short run lasts only about 6 weeks. What the Bank of Canada is really doing is targeting inflation. And a very important part of the Bank of Canada's monetary policy is its communications strategy. It tells people, at every opportunity it can get, that it is going to do whatever it takes to keep inflation coming back to its 2% target in the "medium term". It wants to focus people's expectations of monetary policy on that 2% inflation target, not on the overnight interbank lending rate over the next 6 weeks which, by itself, is nearly irrelevant to most people anyway. "In the longer run, the Bank of Canada sets the inflation rate at 2%" is a much better description of Canadian monetary policy than "for the next 6 weeks, the Bank of Canada will probably keep the interbank lending rate at 1%". And between that long run and very short run, what the Bank of Canada does is adjust the supply curve of reserves, and with it the overnight rate target, to try to keep income moving towards what the Bank thinks is "potential output", which is what I have called Y*.

The LM curve does not have a fixed slope. The slope of the LM curve is whatever the central bank wants to make it. The slope of the LM curve depends on how the central bank adjusts the supply of reserves in response to changes in interest rates, real income, inflation, and anything else the bank looks at when it decides what it needs to do to hit its target. And that depends on the time-frame. In normal times, I would say that the Canadian LM curve is vertical. It's vertical because the Bank of Canada makes it vertical. It's vertical because the Bank of Canada responds to IS shocks by doing whatever is needed to keep the demand for output equal to potential output, which it needs to do to prevent inflation moving away from target. A shift in the IS curve, with potential output unchanged, will have no effect on income. Simply because the Bank of Canada won't let it have any effect on income. That is equivalent to an LM curve that is vertical at Y*.

What about the Fed, right now? Well, we don't really know what the Fed is targeting. I'm not sure the Fed knows either, because different people at the Fed seem to have different opinions on what the Fed should target. Lacking any clearly-communicated strategic target, people can only focus on the Fed's short-run tactics. That's all there is. People have to try to infer the Fed's strategy from looking at its tactics. That's a problem, if the main way that monetary policy works is by influencing people's expectations of future demand, and prices, as well as future interest rates.

Here's my inference of the Fed's current strategy. It is unwilling or unable to communicate credibly any long-run target. If the recession looks like getting worse, it is willing to take what it considers to be extraordinary measures to stop it getting worse. But it is not willing to take those same extraordinary measures to make it better. I think the Fed currently has a sort of tipped-over L-shaped LM curve. The lower bit is near-vertical, and the upper bit is near horizontal. It wants higher than 0% interest rates, but it doesn't want the recession to deepen any further. So people expect the Fed won't let the recession get worse, but don't expect the Fed to make it better. Only if income increased back to full employment would the Fed's LM curve go vertical again.

But anyway. Look at the upward-sloping IS curve. Look at the positive natural rate of interest. Look at the 0% current rate of interest. Would you describe that as a "liquidity trap"?

My own answer is: well, you can call it whatever you like. But there is nothing there that says a return to full employment would require either we shift the IS curve (use fiscal policy) or else have negative interest rates. The Zero Lower Bound does not make it impossible to have an equilibrium at full-employment income.

And all that is leaving aside the question of whether we can escape the liquidity trap by reducing real interest rates by promising higher inflation.

(This post is sort of a response to Brad DeLong and Steve Williamson.)

Comments

[Patrick]

I don't know, but something has to give, 'cause this is just getting weird: Daily Treasury Real Yield.

I want to know why people are basically paying the US Treasury to store their money for them? Is their a shortage of mattresses?

[jesse]

Japan has had low unemployment but has been characterized as hitting ZLB. How is that resolved?

[rsj]

Nick,

I think what Brad deLong was arguing was that the natural rate of interest is *less* than zero.

In general, I am confused about what is short run and what is long run in your graph. I understand how you would argue that the long run LM curve is vertical, but then why would the long run IS curve be upward sloping, and why aren't you using the "long run" interest rate (e.g. 10 year bond yields) and comparing it to the long run natural rate?

I am going to channel Keynes. Then you can complain about old school Keynesians taking over comment threads :P

Divide overall savings demands into two buckets -- demand for short dated assets and demand for long dated assets.

The first demand can be thought as demand for liquidity, which I will call "money", as commercial paper and bills are basically money. Borrowers sell those bonds in order to perform cash-flow management -- inventory investment, working capital, etc. They do not sell those bonds in order to make long term investments.

In a recession, the short rate might be very low, but the expected future short rates are high (when the recession ends), so rates are expected to increase, which means that long dated bond holders are expecting capital losses, subtracting from the demand for long dated bonds and increasing the demand for short-dated bonds -- e.g. "money". Within the overall savings bucket, demand shifts towards the short end.

But simultaneous to this, firms find themselves with excess inventories and their supply of short-dated bonds decreases.

So the equilibrium price of short-dated bonds may well be zero -- can easily be zero -- and still there can be an excess demand for short-dated bonds at that zero price, while the interest rate for long dated bonds might be well-above the natural rate.

Rational investors would prefer to avoid the capital losses from holding long dated bonds and get a zero return in short-dated bonds, whereas rational borrowers have no need of selling short dated bonds as their cash-flow management needs have been met, but they do not believe that they can profitably invest in longer term assets at the current long rates.

I don't really believe that this is the whole story. But it is a counter-argument to your graph. Basically your graph is too under-specified to refute the liquidity trap model.

[Bill Woolsey]

I don't like the upward sloping IS curve.

I just think it is better to have today's IS curve shift based upon tomorrows expected real income and output.

In your previous post, I would say that if we imagine increased current real income causing real consumption plus investment to rise more than real income, then the IS curve is prefectly elastic with respect to the real interest rate.

Real interest rate falls, real expenditure on output increases an infinite amount.

Real interest rate rises, real expenditure falls to zero.

You don't get to upward sloping IS.

I realize that you are making output and income the independent variable.

Still, I would like to be able to use the IS curve and potential output to think about changes in the natural interest rate. People choose to save more, the IS curve shifts to the left, and the natural interest rate falls.

With your IS curve, people choose to save more, the IS curve still shifs to the left, and the natural interest rate rises. Right?

I don't think that is right.

And if I can't use the IS curve to think about changes in the natural interest rate--it loses much of its value to me.

Also, Mr. debtor, why don't we just mandate lower interset rates to benefit you personally? Well, the lower the interest rate the more various people spend, and if the interest rate is "too low," then what everyone wants to spend adds up to more than we can produce.

Why, Mr. creditor, can't we raise interest rates so you can earn a better retirement income? Welll, the higher the interest rate, teh more various people want to spend, and if the interest rate is "too high" what everyone wants to spend fails to add up to what we can produce.

Your diagram can't show that. And you agree it is true (I think.)

So, what is your diagram good for? If real income is below capacity, and it begins to increase, then real interest rates must rise or else real expenditures will surpase capacity.

Is that true if people expect it to be temporary?

Suppose we are at equilibirum. If people expect more output and income in the future, saving falls and investment rises, the IS curve shifts right, and the natural interest rate rises.

Suppose we are at disequilibrium. If people expect more output and income in the future, saving falls and investment rises, the IS curve shifts right, and the natural itnerest rate rises.

Suppose we are in equilibrium. Potential output rises, but it is temporary. Saving rises, and I don't know about investment, but the natural interest rate falls. (With your positive slope, it would rise?)

It just seems to me you are showing a process where output starts to rise, and people expect the recession is finally over, and so expected future income and output rise, and so, the IS curve shifts right, and the natural interest rate rises.

[Andy Harless]

The vagueness of the "rate of interest" reference is a problem for me in this framework. When I think about what would happen if the IS curve shifted downward, I realize this would imply a negative interest rate (if the LM curve is vertical), but that isn't really what would happen: rather, the Fed would get more creative about ways to stimulate the economy, which might or might not result in certain interest rates going lower but certainly wouldn't result in some particular interest rate that is already near zero going negative.

But leaving that issue aside, I think what we have here is a multiple equilibrium model. The Fed's LM curve (actually I would call it a reaction function, but whatever) is shaped like a tangent function, with vertical asymptotes at (or just above) full employment and at the Fed's "OMG we can't let that happen" level of output. The upward-sloping IS curve crosses the LM curve in two places. Maybe the bad equilibrium is stable but the good one isn't?

[JCE]

NIck I have a question.

Didn't the Cambridge debates on the theory of capital invalidate the notion that a 'natural rate of interest' exists? Why is it still prevalent in macroeconomics? (Even Samuelson (1966) concluded as much)

Why did macroeconomists forget (ignore?) the results of that debate?

[Nick Rowe]

Patrick: Yep, it seems to be getting (very) bad again. I don't think it's so much a shortage of mattresses as fear of theft. Plus safety deposit boxes aren't free either. And it's hassle getting your cash into and out of one. Though what you quote there are real rather than nominal rates.

jesse: I don't know much about Japan. I've read a few posts recently on it. It might just be that the gap between Y and Y* is smaller in Japan than in the US. It might be that Japan's IS curve is fairly flat, because of their demographics. It might be that Japan's unemployment rate isn't measuring the same thing as other countries'; because Japan's unemployed either quit the labour force (become housewives?); or because they get any job they can get, even if it isn't very productive. I don't really know.

rsj: Yes, Brad DeLong, Paul Krugman, and almost everyone else, believes the natural rate is less than 0%. That's because they draw a downward-sloping IS curve. (Paul Krugman drew a graph just like mine about a year ago, except his IS curve sloped down, as they normally do, and so his natural rate was negative.)

That's where my picture is different. That's what this post is about. My natural rate is above 0%, even though the actual rate is 0%, even though we are below full-employment income.

You are talking about the term structure of interest rates. Sure, long rates are still positive, even while short rates are 0%. I want to explain why the whole yield curve is so low.

[Nick Rowe]

Andy: You are thinking *very much* along the same lines.

Agreed it's a "reaction function" really, as much as an LM curve. The LM curve depends as much on the money supply function as on the money demand function.

"But leaving that issue aside, I think what we have here is a multiple equilibrium model. The Fed's LM curve (actually I would call it a reaction function, but whatever) is shaped like a tangent function, with vertical asymptotes at (or just above) full employment and at the Fed's "OMG we can't let that happen" level of output. The upward-sloping IS curve crosses the LM curve in two places. Maybe the bad equilibrium is stable but the good one isn't?"

Yes. Multiple equilibria. But (as nearly always) I think there are *3* equilibria. 2 locally stable, with an unstable one in the middle. LM steep in QE territory, where it crosses IS where we are now, which is stable, then flat at 0% (no QE) so it crosses IS again, which is unstable, then it goes vertical at full-employment, so you get a third, stable equilibrium at the natural rate. Something like that.

[Too Much Fed]

Are you assuming real GDP should grow by the same amount as real aggregate supply?

[Nick Rowe]

Bill: "I just think it is better to have today's IS curve shift based upon tomorrows expected real income and output."

We *could* think of it that way, but: it's simpler to explain and draw the curves my way; and, "tomorrow" really starts today, and if there is no anchor for people's expectations (because nobody knows what the f*** the Fed is doing), then expecting tomorrow's income to be the same as today, until something convinces you otherwise, seems fairly rational. Especially since this is all new for most people.

"In your previous post, I would say that if we imagine increased current real income causing real consumption plus investment to rise more than real income, then the IS curve is prefectly elastic with respect to the real interest rate."

The maths says it slopes up. Because the 1/(1-mpc-mpi) term now becomes negative. And the slope is the inverse of (the interest-elasticity of demand times 1/(1-mpc-mpi). (Me, of all people, resting my case on math!). Suppose we derive the IS curve from the loanable funds diagram. As Y increases, the Sd curve shifts right, as usual, but now the Id curve shifts right too, and shifts more than the Sd curve. So r at the intersection rises, rather than falls.

Or, if we derive the IS curve from the keynesian Cross, the AE curve is steeper than the AE=Y line. An increase in r shifts the AE curve down, as before. But that now shifts the intersection of the two curves to the right.

"People choose to save more, the IS curve shifts to the left, and the natural interest rate falls."

Now it becomes: people choose to save more, the IS shifts to the *right*, and the natural rate of interest falls. Intuition: you can use the same loanable funds graph, and hold Y constant this time, so r* falls. Or, use the KC graph, the increase in Sd shifts the AE curve vertically down, so equilibrium rises, for a given r, so IS shifts *right* when Sd rises.

Creditors/debtors: "And you agree it is true (I think.)"

Yes, I agree it is true. Maybe, not all diagrams are good for all purposes? I'm still feeling my own way around this one. It feels weird to me too.

"Is that true if people expect it to be temporary?"

The more permanent that people expect the current level of demand to be, the more likely the IS is to be upward-sloping. It's standard to recognise that mpc gets bigger as the change in Y becomes more permanent (Friedman). Just say something similar about mpi, and when you add them together the sum could easily exceed one.

Mull it over now you see that the IS curve *shifts* the wrong way when it slopes the wrong way. I may not have addressed all your points fully. But it's better for me to wait for your response on that point first.

[Nick Rowe]

JCE: I may be muddled here: are you the Sraffa(ish) guy, who has a blog? If so, there's something I wanted to ask you on that topic. (Or maybe I'm just confused).

In any case, let me know, so I know where you're coming from when I try to answer your comment, as well as ask my own question.

[Nick Rowe]

TMF: I am saying that I *want* output to be and grow (at least approximately) the same as aggregate supply. I am certainly not assuming it *will* do that.

[Too Much Fed]

Nick, I believe you need to ask why real GDP may not grow as fast as real aggregate supply.

For example, is it possible that most goods have gone from mostly supply constrained to mostly demand constrained, meaning that productivity gains and other things lower employment instead of going into increased supply/output?

[rsj]

Oops, in the above, I should have said, say it is 4%, as that is the amount used in the rest of the post. Anyways, you get the picture.

[Nick Rowe]

rsj: you lost me on the 4%. Would you like to copy and paste, do a new corrected comment, then I will delete the old?

TMF: Y fell below LRAS Y* because AD fell.

[Bill Woolsey]

I think part of my problem is that I don't derive the IS curve from the Keynesian Cross.

I have no good reason to call it "IS". It just shows the negative relationship between the real interest rate and real expenditure. What would happen if somehow real output adjusted with real expenditure and that had feedback on consumption and investment (mpc+mpi) just really doesn't get involved.

I understand, however, that with a supply of saving and demand for investment diagram, the increase in the supply of saving to the right leaves the natural interest rate lower. And so, your IS curve shifts "down," which is to the right.

But anyway, I don't have any simple diagram to show that an expansionary monetary policy can increase real interest rates.

Do you not like having a negative natural interest rate?

[rsj]

Nick, OK:

Say that the natural rate -- which is a long term rate -- is normally 4%. But in the current period it needs to be 2%. In the current period, only at 2% will enough capital investment occur to ensure full output.

The capital stock lasts, say, 20 periods, and is financed with 20 period debt.

Assume people believe that the recession will last 2 periods, and after that, the economy will get back to normal. Then they must believe that the CB will raise the short rates starting in period 3, back to the normal level of 4%. (We are ignoring risk premiums here, so long rate = average of short rates). We are also ignoring any "ramp up" or ramp down of the short rates. Those are just complications.

What short term rates can the CB set for 2 periods, so that the average of those rates, plus 18 periods of 4%, averages out to 2%?

r*2 + 18*4 = 20*2

r = -16%

As the CB cannot set a nominal rate of -16%, the long rates will be too high and there will be a recession.

But if people believe that the recession will last 7.8 periods, the CB credibly promise to set the short rate to 0 for that time, and then back to 4% when the economy recovers, so that the long rate will be 2%, which is what is necessary for the savings/investment market to clear in the current period.

This is the reverse of a tinkerbell effect. Households and the CB need to be sufficiently pessimistic in order for the long rates to drop to the market clearing rate fast enough. If households have sticky expectations, or adaptive expectations, then there will be a recession due to the interest rate being too high, even though the natural rate is positive.

[Nick Rowe]

Bill: "Do you not like having a negative natural interest rate?"

It could be negative, in principle. But what was the big shock in 2008 that suddenly made it go from positive to negative? Scott's answer is that the big shock was monetary policy tightened (his "monetary policy sets NGDP" vertical LM curve shifted left). And that is what caused the actual rate of interest to fall. Now, partly that was just a fall in the nominal rate, due to lowered expected inflation. But I think it was the real rate too that fell. This post is saying that tight monetary policy can also cause the actual real rate to fall below the natural real rate. My picture is just a picture of Scott wearing Keynesian clothes. He looks a bit funny, but I think he's still there.

"What would happen if somehow real output adjusted with real expenditure and that had feedback on consumption and investment (mpc+mpi) just really doesn't get involved."

I think it has to get involved. There's too much Clower in me to leave it out. If demand falls, people and firms will be on the long-side of the output market, and will find themselves sales-constrained. That will impact people's constrained (effective) consumption demand functions, and firms' constrained investment demand functions. The Old Keynesian IS curve used to show this, by incorporating the Old Keynesian multiplier process. It sort of got lost in the New Keynesian IS curve, I think. And if the IS curve is going to tell us what happens when we are away from the natural rate of income, it has to incorporate this feedback. (My own IS curve, by the way, is total rubbish to the right of full-employment, because it will be the buyers not the sellers who are quantity-constrained (unless we have imperfect competition) but I didn't want to get into that.)

[Nick Rowe]

JCE: On second thoughts, I decided my answer to your question wouldn't change much whether or not you are who I think you are.

Don't take my answer as authoritative.

As far as I can see, the Cambridge-Cambridge Capital Controversy has had almost zero impact on modern macroeconomics. My guess is that not many have much knowledge of that debate. (I have *some* knowledge, through my own curiosity 30 years ago, but not much). The existence of a natural rate is treated as unproblematic. There is some possibility allowed that monetary policy might have some long-run non-neutralities, (multiple equilibria), but even here the focus is more on natural rates of output and unemployment, rather than on the natural rate of interest itself (though one would almost always imply the other).

The concept and existence of the natural rate of interest plays a central role in modern Neo-Wicksellian/New Keynesian macroeconomics. Far more so than in older monetarist and keynesian perspectives.

In my own case, recently I made the more modest critique that the natural rate may exist, and be unique, but we cannot come anywhere close to observing it in real time. And we cannot hope to predict it very well, because the natural rate depends on almost everything in the economy, and will vary over time for reasons we cannot in practice determine. It is not some God-given physical constant.

http://worthwhile.typepad.com/worthwhile_canadian_initi/2011/06/y-tu-natural-rate-of-interest-tambien.html

So any monetary policy in which it plays a central role will have serious practical difficulties.

And that's leaving aside the problem that different financial assets will have different natural rates, and the spreads between them may vary over time, especially in a financial crisis.

Now, funnily enough, there is one small exception *I know about* (others may know of others) to my statement that macroeconomists ignore CCCC. David Laidler recently wrote a paper for the CD Howe that explicitly used CCCC to critique the Neo-Wicksellian monetary policy of the Bank of Canada. And David is a monetarist!

http://cdhowe.org/defining-%E2%80%9Cneutral%E2%80%9D-level-for-interest-rates-a-smoke-and-mirrors-game/14269

I, personally, remain unconvinced by the Cambridge critique. *As far as I can see*, if a Walrasian/Arrow-Debreu equilibrium exists, and is unique, it defines within it a natural rate of interest (subject to qualifications in my question below). *As far as I can see* a lot of the CCCC debate was really about whether the natural rate could be determined *independently of preferences*. And (outside of very special one-good Y=F(K,L) models) it cannot. So what? I say. Preferences matter too, in determining relative prices including intertemporal prices like interest rates.

BUT, the chances of getting a nicely-well-behaved downward-sloping Investment demand function (and hence IS curve) out of anything other than a one-good model? I wouldn't bet on it. But my hunch is that the complications that arise from firms being sales-constrained (ignored in the Walrasian model) are more important than anything coming out of CCCC. Hence this post.

Now, my question: I never found Sraffa easy to understand. Sraffa said (I think) that the natural rate on wheat would, in general, be different from the natural rate on barley. Right? If so, is this what he meant:

Suppose the relative price of barley against wheat is rising at (say) 1% per year. Then, under perfect competition, and free flow of capital across sectors, the barley natural rate of interest must be one percentage point lower than the wheat natural rate of interest.

Is that what Sraffa was saying? (With all due allowance for over-simplification?)

[Too Much Fed]

Nick's post said: "TMF: Y fell below LRAS Y* because AD fell."

IMO and to see why AD fell, the budgets of the major economic entities need to be examined.

[Nick Rowe]

rsj: You lost me a bit there. Right at this bit: "Assume people believe that the recession will last 2 periods,..."

Suppose, just suppose, the central bank can set negative rates of interest. And it knows the natural rate. By definition (OK, by *one* definition of the "natural rate", and the one I am using in this post), if the central bank sets the actual rate at the natural rate, there won't be a recession.

But I think I see where you are going. Suppose some real shock to savings and investment lowers the 20 year natural rate for 2 periods, from 4% to 2%. Then it goes back up to 4% and stays there forever. Pure expectations hypothesis of the term structure, and perfect foresight after the initial shocks hits. That would require the central bank to set a negative short term rate for 2 periods to prevent a recession.

Now suppose it can't do that. Suppose the lowest it can set is 0%. OK, looks like maybe a recession. But then you lost me at this bit:

"But if people believe that the recession will last 7.8 periods, the CB credibly promise to set the short rate to 0 for that time, and then back to 4% when the economy recovers, so that the long rate will be 2%, which is what is necessary for the savings/investment market to clear in the current period."

If the bank sets 0% for 7.8years, wouldn't that mean a boom in the third year, because the short term rate will still be zero, so the 20 year rate will be less than 4%, and so below the natural rate?

[Nick Rowe]

TMF: You are off-topic. Please stop. Do not respond to this comment either.

[Too Much Fed]

Nick's post said: "And that's leaving aside the problem that different financial assets will have different natural rates, and the spreads between them may vary over time, especially in a financial crisis."

Is it a sign of wealth/income inequality (or some other "imbalance") if an economy needs one set of interest rates above 5% to prevent asset price speculation and another set of interest rates below 2% for the real economy?

[Bill Woolsey]

Rich people save. Saving is good. It allows for lower interest rates. The lower interest rates allow for more capital accumulation. This allows for higher productivity and higher real wages.

Ah.. but we can come up with examples where there is capital reswitching. Lower interest rates can result in a switch from processes that provide lots of consumption now and in the distant future, in the favor of projects that have less consumption now and in the more distant future. Now, if interest rates are low enough, like zero, then we go with the same project we go with the higher interest rate.

So.. this is is the key part... saving isn't good. rich people aren't good. having the red unions raise wages to completely wipe out income from capital is the right approach. And we must rationally plan investment to pick the better projects.

[Bill Woolsey]

I think the real interest rate on short and safe assets went negative because people expected a deep recession. Households expected lower income in the future, so saved more. Firms expected lower output in the future, so they invested less. Natural interest rate fell. Negative for the short and safe ones. Worse, there was a shift away from risky assets to short and safe assets, pushing the natural interest rate on the short and safe assets even more negative.

If economists, the Fed, the politicians, had all agreed that the Fed could and would keep nominal expenditures on a stable growth path, and quickely reverse any deviation, then perhaps expectations would have been reversed.

Instead, we had a dominant message of the Fed is out of ammunition. Some said we needed massive government spending, but others said it wouldn't work. Some said we had to jumpstart the shadow banking system, repos funding mortgage backed securities. Others said that was impossible, because the assets are bad.

Looks worrisome. Save more. Invest less. Hold T-bills and FDIC insured deposits. Wait and see.

So, negative natural interest rate on short and safe assets.

In my view, the best solution would be a negative nominal rate on short and safe asset. Second best is quantitative easing, purchasing lots of long government bonds. Get NGDP back to target and then say, see, we can do it even if some if bank after bank is being reorganized, and we plan to do it in the future too.

[Nick Rowe]

Bill: there are (at least) two different definitions of the natural rate:

1. What would equilibrate desired saving and investment given the actual level of income and actual expectations for future income.

2. What would equilibrate desired saving and investment if income were at the natural rate (LRAS) and were expected to remain so.

You are using it in sense 1; I am using it in sense 2. But we are saying the same thing. Tight monetary policy lowers actual and expected income and lowers the natural rate in sense 1, and lowers the actual rate below the natural rate in sense 2.

Those re-switching examples never seemed to me to pay enough attention to the term structure of interest rates. There was always a flat term structure assumed. Not to mention how the term structure of investment would interact with the desired term structure of saving and consumption at the aggregate level, to create a term structure of interest rates.

[JKH]

Your upward sloping IS curve seems like a “forward” IS curve, carved out by future rightward shifts in the “spot” IS curve, where such future shifts are associated directly with future incremental interest rate increases and corresponding income increases. The “forward” IS curve consists of those pairs.

[Nick Rowe]

JKH: that, I think, is how Bill wants to look at it too.

Suppose current demand Yd depends on current income Y and expected future income Ye, as well as the rate of interest r. Yd=D(Y,Ye, r). You could define a short-run IS curve as combinations of Y and r such that Y=Yd=D(Y,Ye,r). Then changes in Ye would shift that IS curve. And you could define a longer run IS curve as combinations of Y and r such that Ye=Y=Yd=D(Y,Ye,r). Question: how long is the period? If you make the period very short, Y drops out altogether as having any effect on Yd. It's all in Ye. Make the period longer, and Ye gets incorporated into Y. It all depends on how long people expect the recession to last, and how good current income is as a proxy for future income. The longer it is expected to last, and the better the proxy, the more upward-sloping it gets.

[rsj]

Nick @9:34,

"Pure expectations hypothesis of the term structure, and perfect foresight after the initial shocks hits. That would require the central bank to set a negative short term rate for 2 periods to prevent a recession."

No, I am not assuming perfect foresight. Merely that people believe the recession will last for 2 periods, and that short rates will go back to normal after that. We don't know how long the recession will actually last, and we don't need to know. All that is relevant is the current natural rate that clears savings and investment, and what the expectations are for future short rates, to see whether the current long rate will be at the level that clears savings and investment, or whether it will be at some other level. We also don't need pure EH, I just assumed it to make the math simpler. Once you start adding positive or time-varying risk premiums, then the job of the CB becomes harder.

The economy needs investment in long term assets each period, but the CB can only credibly promise to adjust short term rates based on the current economic conditions. It cannot promise to keep short term rates low long enough to justify enough current period investment in long term assets in all cases. Anytime the market clearing rate on long term assets moves around (say based on changing expectations of long term profits, or long term incomes), then the CB will invariably find itself in a situation in which it cannot adjust IR policy to get the right long term rates that clear savings and investment demands. It doesn't have the right tool to adjust long term rates quickly in real time.

The 7.8 periods was just a comment that people need to believe that the recession will last for 7.8 periods (again, we are not assuming perfect foresight, since we know that the recession will last for 2 periods). But if people, in the current period, believe the recession will last for 7.8 periods, and that the CB will keep rates at zero, then the recession can be avoided as long term rates drop to 2%. So excessive pessimism can avoid the recession, if it is matched with confidence that the short rates will be so low. That is what I meant about a reverse tinkerbell effect.

[Bill Woolsey]

I always go with the natural interest rate being the level of the interest rate where saving equals investment if real income equals potential output, but given existing expectations.

I don't like requiring correct expectations, though my worry is more about correct expectations regarding the profitability of investment.

Given where people are now and what they happen to think they and other people are now, what level of interest rate would make all of their spending plans add up to match the productive capacity of the economy?

I don't, however, have in mind the level of the real interest rate that will make their planned expenditures add up the the current level of output, wherever that might be.

[Max]

"This is the reverse of a tinkerbell effect. Households and the CB need to be sufficiently pessimistic in order for the long rates to drop to the market clearing rate fast enough."

Recently junk bond yields have increased at the same time that long term treasury yields have plunged.

Pessimism does reduce risk-free rates, but is that likely to spur investment?

[Nick Rowe]

rsj: "We also don't need pure EH, I just assumed it to make the math simpler."

Understood. I wasn't complaining about EH. It was the right assumption for you to make.

On Perfect Foresight. I would first work through your example assuming PF and allowing the CB to set negative r. Then I would do PF with a ZLB, just to see what happens. Then I would do ZLB, and relax PF, to see what you would need to assume about imperfect foresight for the CB to be able to keep the economy from going into recession.

But I think I am now getting the gist of your argument. Pessimism might be a good thing in your example.

[Nick Rowe]

Max: "Pessimism does reduce risk-free rates, but is that likely to spur investment?"

That's my thought too. But let's set it aside for a bit, and see where rsj's example leads us.

Bill: OK. I guess I am having a hard time separating expectations about the future level of income from the current level of income. In a discrete time model, where this period and next period are discrete events, this seems to make sense. But as we move to continuous time, so the future starts right now, I expect we would have to talk about an expected time-path that starts from where we are right now. I'm unhappy about assuming correct expectations too. This is one of the problems with getting any sort of tight definition of the Wicksellian natural rate. If people currently expect a time-path in which the recession continues from this point on, does it make sense to talk about what the equilibrium rate of interest would be if we were at full employment right now, but people expected the recession to continue from this point on? There's no way they would expect it to continue, if we weren't in recession right now.

Conundrums.

[JCE]

Nick, no I don't have a blog.

I´m an econ graduate student in bogota, colombia. i´ve just recently finished my masters thesis on wicksell's monetary theory. in it i explored the consequences of the cambridge debate on wicksell's theroy, namely that it invalidates the notion of a 'natural rate' and thus of a real loanable funds market.

[Nick Rowe]

JCE: OK. Sorry, I had you muddled with someone else. Did you see my reply to you above? Did I get it (roughly) right?

[JCE]

Oh i hadn´t seen the reply. Thanks
Yeah, what sraffa said was basically that each good has a different natural interest rate. and that there is no way to aggregate these goods into an homogeneous 'K' so that you have a negative relationship between K and r for the whole economy.

I think this means, further, that the conception of a 'real' market for loanable funds is invalid. saving and investment are monetary phenomena, and so are all interest rates in the economy. in other words, interest rates do not depend on 'real' factors

[JCE]

... all this is also related to the theory of a monetary economy. a line of thought tracing back to the antibullionists assert that in a monetary economy with a fiat currency, the financial system does not need previous deposits (saving) to create loans for investment purposes. (keynes also made this point in the treatise)

i´d be curious to hear you thoughts on this paper http://www.bis.org/publ/work346.pdf which places emphasis on precisely this ability of financial institutions to create credit as a cause of the current crisis

[paine]

great post nick

your IS with a hard on
appeals to the accelerationist in me

i would say however the graph is poetry here
and andy prefers prose

you need a graph in motion to cease the mind clearly here

as you change its policy parameters
and agents change their preferences

[paine]

btw
forget the deeply problematic notion :a natural FE rate

just stick to your upward soaring IS
doesn't it suggest the path to full employment output is
also a path of rising borrowing rates
as the production system explodes out of its near paralysis
and the credit authorities yank fast to keep the system's
prices from racing away from out put growth tha if indeed investment triggered will likely create serious shortages
even as it retains serious slack

a sudden shift to war economy controled not by quantitative rations but by prices and borrowing rates might look like this

i don't however think japan does or the US

[paine]

we marxicocals would call this feldman expansion where a previously winnowed
department one takes off
even as department two
given the wage goods slack plays belated catch up

note closed system assumption really bites in here

open this puppy up and you get a gig-normous import tsunami
of foreign built machinary

[Marc Labbe]

When things get complicated, arduous, etc....; there are always a KISS solution..

http://www.washingtonsblog.com/2011/07/we-have-forgotten-what-ancient.html

[K]

JCE: "I think this means, further, that the conception of a 'real' market for loanable funds is invalid. saving and investment are monetary phenomena, and so are all interest rates in the economy. in other words, interest rates do not depend on 'real' factors"

Whoa! What about productivity and the size of the labour force? Technology and demographics (and, short term, changes in preferences like leisure and paid/unpaid employment) are the *real* determinants of the natural rate. Everything else is just relative price.

[Andy Harless]

3 equilibria, yes. An interesting implication is that the response to fiscal policy is discontinuous. On the margin, at one of the stable equilibria, the fiscal multiplier is very small, but at the unstable equilibrium, it becomes infinite. (That is, it's infinite when the IS curve is tangent to the LM curve, because any small upward shift in the IS curve eliminates the bad equilibrium and moves you to the good one.) So Scott Sumner is right that the stimulus was ineffective because the Fed moves last, but Paul Krugman is also right that a much larger stimulus would have been effective. I seem to recall Woodford having a model with a similar property (although in that case the lower stable equilibrium was deflationary because there was no unconventional monetary policy to prevent deflation).

[Rob Parenteau]

If you want to frame the current US situation in IS-LM, which has some real problems as a modeling strategy, not the least of which is a flow and a stock equilibrium inhabit two different units of time (an interval and a point) you are much better off working with a near vertical IS curve, since a) the Fed pegging 2 year UST at fed funds rate until summer 2013 brought longer dated UST yields and private market interest rates (like mortgage rates) down, and that is surely not consistent with liquidity trap/horizontal LM diagnoses, and b) housing and capital spending have proven fairly interest rate insensitive, real or nominal wise, which is what you might expect after serial asset bubbles and balance sheet recessions, when CEOs and institutional investors face ultra myopic incentive structures, and 25% of homeowners are upside down/underwater. But this is a hard one for the New Keynesians to grasp, because it means there is not a magical real interest rate level that will get you back to full employment, and you have to find measures that can effectively shift the near vertical IS schedule...say like an employer of last resort based fiscal policy...because hey, that is the short cut to Weimar, right?