New York Times: "Swedish Bank Move Creates a Global Shudder"
David Beckworth: "China's Coming Devaluation: Another Consequence of the Fed's Mistake of 2015"
Market Watch: "Is this the week central banks lost their market credibility?"
Zerohedge: "This is What Central Bank Failure Looks Like"
Scott Sumner: "Another Sign of Fed Incompetence"
I think you get the idea. What's going on? Well, I hate to pick on the Swedes, but the Swedish Riksbank is one of my favorite examples. As I discussed in a previous post, the Riksbank has a 2% target for inflation, but actual inflation has been in the neighborhood of 0% for about 3 years, though the Riksbank appears to be committed to returning inflation to target. On February 11, the Riksbank reduced its policy rate target by 15 basis points to -0.5%, and issued a statement, which reads in part:
The economy continues to strengthen but inflation is expected to be lower during 2016 than previously forecast. The period of low inflation will therefore be longer. This increases the risk of weakening confidence in the inflation target and of inflation not rising towards the target as expected. To provide support for inflation so that it rises and stabilises around 2 per cent in 2017, the Executive Board of the Riksbank has therefore decided to cut the repo rate by 0.15 percentage points to −0.50 per cent. Purchases of government bonds will continue for the first six months of this year, in accordance with the plan adopted in October. The Executive Board has also decided to reinvest maturities and coupons from the government bond portfolio until further notice. There is still a high level of preparedness to make monetary policy even more expansionary if this is needed to safeguard the inflation target.This is a very familiar story in many countries, including the U.S. Inflation is not increasing as the central bank had been anticipating, and in the Riksbank's case a decision has been made to take corrective action. That corrective action is more of the same - pushing the policy rate further into negative territory, and conducting further quantitative easing. As well, there is forward guidance: the Riksbank will do even more of the same if they don't get results.
The Riksbank seems to have an orthodox view of how the inflation process works:
Growth in the Swedish economy is high and unemployment is falling, which suggests that inflation will rise in the period ahead.Basically, the Riksbank believes in its Phillips curve. For it, lower unemployment means higher inflation and, presumably, it thinks a lower nominal interest rate will further reduce unemployment and increase inflation. So, that's a fairly typical view. Central banks experiencing low inflation are typically the ones who have done the most to put unconventional policies into practice - negative nominal interest rates and quantitative easing in particular.
Most of the people currently calling the Fed stupid are orthodox types. They have a Phillips curve view of the world, and they think of low nominal interest rates as "accommodative." And orthodox central banking views breed a "whatever it takes" set of actions - negative nominal interest rates, quantitative easing - in an attempt, as they see it, to get inflation back to target.
Noah Smith, who has been watching these things for a long time, seems puzzled and gloomy. Here's the puzzlement:
The more important point, though, is that no one really knows what is going on with monetary policy right now. No one knows what the Fed is really trying to accomplish, or what it can accomplish, or how to go about accomplishing it. Is it still set on raising interest rates in order to avoid the semblance of abnormality from keeping them close to zero? Is it worried about demand-side shocks from China’s slowdown? Does it want the public to think that it will never let inflation go above 2 percent, or does it want us to think that 2 percent is in the middle of the acceptable range? Is it trying to raise inflation and failing? And if it did want to raise inflation to 2 percent, would it do so by keeping interest rates low, or by raising them?Here's the gloom:
It’s becoming clearer that the Fed's experiments during the Great Recession, dramatic as they were, taught us little about how monetary policy works.Now I'm puzzled. Noah is a guy who loves experiments and empirical work, and thinks every econ 101 student should spend a lot of time staring at data. In the last 9 years, we have had a major financial economic event, coupled with major central bank crisis intervention, followed by an unusual recovery, sovereign debt crises, and many central banks experimenting with unconventional policy. But "us" did not learn anything. Go figure.
Here's something I've learned since the financial crisis. There's a paper by Benhabib, Schmitt-Grohe, and Uribe (BSU), "The Perils of Taylor Rules," that shows how an aggressive Taylor-rule central banker inevitably converges to the zero lower bound, and gets stuck there. A central banker following a Taylor rule sets a target for a short-term nominal interest rate, and increases that target interest rate if the inflation rate increases relative to its target level. Typically, Taylor rules include a term for the "output gap," but the argument doesn't depend on that. Basically, a typical Taylor rule embeds orthodox central banking - increasing the nominal interest rate should make the inflation rate go down. Further, an aggressive central banker is one who follows the "Taylor principle" - if the inflation rate increases relative to its target, then the nominal interest rate should go up more than one-for-one. Why? Again, that's part of orthodox central bank thinking. If the nominal interest rate increases more than one-for-one with an increase in the inflation rate, the real interest rate should go up in the short run, real economic activity should go down, and by orthodox Phillips curve logic, the inflation rate should fall.
But, if you work through BSU, you'll see that this results in many dynamic paths that end up at the zero lower bound (ZLB) for the nominal interest rate, which is a steady state. Once there, the orthodox central banker is stuck. Inflation stays below target, as there's nothing to make it go up, but the orthodox central banker is convinced that a lower nominal interest rate is what's needed to increase the inflation rate, and gets increasingly frustrated. Some people can see these things right away, but I usually have to work it out myself to understand it. I wrote this paper with David Andolfatto, which adds some stuff to BSU, including a scarcity of safe assets and low real interest rates.
If you understand BSU, it's only a short step to understanding the current behavior of central bankers. Frustrated by what they see as a ZLB problem, orthodox central bankers find other ways to be "accommodative." If you think about it a bit, or talk to Miles Kimball, you'll understand that zero isn't really a lower bond for the nominal interest rate - the orthodox central banker can go negative, as the Bank of Japan, the Danish central bank, the ECB, the Swiss National Bank, and the Swedish Riksbank have done. He or she can engage in quantitative easing (QE) - central bank purchases of various long-maturity assets, as the Fed, the Bank of England, the Swedish Riksbank, the Swiss National Bank, and the Bank of Japan have done. The orthodox central banker can also make promises about the future, in the hope that those promises are believed, and will have some effect today. And, the central banker who does not do those things, does them and stops, or doesn't do "all it takes," will find plenty of people willing to call him or her stupid (see the links at the beginning of this post, or see Narayana's web page). So, if you read BSU and thought that it would be easy for a central banker to get out of the low-inflation, low-nominal-interest-rate trap, better think again.
So, what should happen as central bankers fall into the ZLB, or ELB (effective lower bound) trap? Ultimately, people should start to understand that low inflation will persist for a very long time, and this will show up as low yields on nominal government bonds, and low anticipated inflation, by whatever measure. Here are 10-year yields on U.S. Treasuries, Japanese government bonds, and Swedish government bonds:
For the U.S., if we look at the 10-year bond yield and 10-year TIPS yield, we see:
So that's ominous, and the reaction of a committed orthodox central banker is to just dig a deeper hole, as reflected in the Riksbank's statement earlier in this post. Lower measured anticipated inflation is just like lower actual inflation - it means greater frustration on the part of the orthodox central banker, and he or she wants to go more negative, and buy more assets, cheered on by various Kimballs, Kocherlakotas, etc.
What are the lessons for people outside central banks?
1. If you live in Sweden, for example, don't pay any attention to the Riksbank's forecasts. Pay attention to what the Riksbank says. Inflation is actually going to stay low - zero for a long time would be a good forecast I think - and the Riksbank is trapped in the hole that it dug for itself.
2. If the central bank starts using words like "Fisher effect," pay attention. This central bank means business.
3. Once stuck at the ZLB or ELB, there's nothing for the central bank to do. That's what I mean by "the end of central banking." Central banks can purchase all the assets they want - that's not important. What matters is the central bank's nominal interest rate policy target, and the rule for setting it.
4. Beware of other "tools" that people might think up. A recent one is "helicopter drops." More about that later.
5. Beware of changes in central bank objectives masquerading as changes in tools - e.g. nominal GDP targeting, price level targeting, or a higher inflation targets (4% for example). It's typically an orthodox economist or central banker projecting those ideas, which will similarly imply a path to ELB, or sticking there, if that state has already been attained.
6. Don't panic. Zero or negative inflation actually is OK. If someone tries to tell you about the black hole of deflation, plug your ears and start humming.
7. What is not OK is for people to continue to anticipate 2% inflation that a central bank promising but incapable of delivering. Again, for long-range planning purposes, think zero inflation indefinitely.
8. If you're an economist, pay attention to what your models are actually predicting, unless your model is straightforward IS/LM - Phillips curve. In that case, you need to learn some more economics. Standard off-the-shelf monetary models essentially all exhibit a neo-Fisherian effect. That's nothing special. The Fisher effect is important. Typically increases in nominal interest rates lead to increases in inflation. Orthodox people - particularly the ones with some technical facility - can think up examples where they think this doesn't happen. Don't buy it though. If they persist, you can always plug your ears and start humming.
9. For a non-interventionist, the low-inflation policy trap is a wonderful thing (John Cochrane, for example, seems to be fine with it). The interventionist orthodox central banker, in the process of trying to "do all it takes," sows the seeds of his or her own destruction, and becomes powerless. No high inflation, no hyperinflation, only low inflation - and inflation might be fairly stable. In the course of committing policy hara kiri, the orthodox central banker imposes some transition costs, but the steady state ain't so bad.
So, if you're confused, worried, or feeling like you haven't learned anything about how monetary policy works, there's no good reason for that. Cheer up.
Addendum: More othrodox central banking. Here's what Draghi said today:
We are very conscious, and wish interest rates could go up again, but this is not the case now. I don’t think anybody is thinking about changing policies, but if we were to change, it will lengthen the timing of inflation reaching 2%.
I think maybe many , if not most , central bankers are being a bit disingenuous. What if their primary target is not inflation , or employment , but leverage ? What if they've at long last internalized the mathematical truism that debt/income ratios can't grow to the sky ?ReplyDelete
Sweden has expressed a concern about household debt , prompting the "leaning against the wind" pissing contest with Svensson. More and more you see prominent economists at the BIS , BOE , IMF , etc., speaking honestly as they describe monetary policy as being essentially a mechanism for bringing demand from the future to the present , mainly via debt , thus highlighting the requirement that credit is rationed such that self-sustaining new sources of income are produced with that debt , rather than falling back on our past reliance on debt-fueled consumption and/or asset booms.
Total nonfinancial debt/gdp has been remarkably stable in the U.S. since the official end of the recession , in stark contrast to the rapid rise throughout the 2000-08 period. Is that by accident , or by design ?
What a waste it would be - though good for some giggles if you're in on the gag - if the blogosphere has been engaged in all this high-octane theorizing while the Fed has been ignoring the theories all along , and has simply been focused on the job of keeping a tight lid on leverage.
The Euro area has low inflation. Would you also say that this fine? Looking around I see a catastrophic situation everywhere. A situation which could e.g. be elevated by printing money and giving it directly to governments to spend on pensions, maintaining infrastructure and so on.ReplyDelete
It seams also very unlikely to me that such a policy (printing money and giving it to governments) would not lead to inflation.
First, I don't think it's catastrophic. The only loss here is that the ECB is promising higher inflation (though it's stated goal is softer than a 2% target - they seem to think that something less is OK), but can't deliver it, which confuses people. Uncertainty is not good, but it's not catastrophic either.Delete
Second, I've heard some version of this a lot:
"It seams also very unlikely to me that such a policy (printing money and giving it to governments) would not lead to inflation."
But I'm starting to think this is not correct. If there are excess reserves outstanding, and the CB is pegging the nominal interest rate on reserves, suppose the fiscal authority issues debt to finance transfers, and suppose the CB swaps outside money for this newlly-issued government debt - even imagine this is currency, if you want. Ultimately the newly-printed money end up as reserves, and has no inflationary consequences. That's a hypothesis, and I'm in the process of working that out formally.
If that hypothesis is true then governments can just stop collecting taxes altogether and apply QE-infinity.Delete
No, it doesn't change the tax implications at all.Delete
I suppose it does not change the implications at all because you assume reserves pay the same interest as public debt, so in the end issueing reserves or t bills does not make any difference. The same for cash at zero lower bound.Delete
Still, I do not see how this is not a free lunch if what you say is correct. In practice, you say that the government can issue trillions of trillions of debt without any effect on inflation, if rates are zero. Then, why not just abolish all taxes altogether and finance the government this way? In practice, you allow for an infinetely lasting Ponzi game.
"you say that the government can issue trillions of trillions of debt without any effect on inflation, if rates are zero."Delete
No, I'm just saying it won't make any difference, given a stock of reserves outstanding, if transfers are financed with government debt or reserves, fixing the nominal interest rate. And it doesn't matter if the nominal interest rate is zero or something else.
Steve, in the case of open market operations it is clear why not (it's a swap between one government liability and another paying the same interest rate so nothing changes). But why is a tax cut (helicopter drop) not a free lunch; because of the Ricardian equivalence? Also, if there exists a shortage in safe assets as in your models, wouldn't the government face a free lunch so long as demand for such assets is perfectly elastic and if the impact of the tax cut on income is sufficiently high?Delete
Ok, but I immagine what you say is true only so far as reserves and t bills pay the same interest rate, whatever that rate is. Am I right? Or you think that's true even when reserves pay zero interest and t bills 5%?Delete
Another question is the following. Do you think that interest rates are all that matters for inflation determination? If this is the case, then you think that the government can issue all the debt it wants without any effect on inflation, as long as the nominal rate is pegged. I think that this is a natural limit of a pure neo-fisherian view, that should be addressed. And it is also the reason why I am able to understand neo-fisherism only in fiscal theory of the Price level framework
"Or you think that's true even when reserves pay zero interest and t bills 5%?"Delete
Why would anyone want to hold the reserves then?
"then you think that the government can issue all the debt it wants without any effect on inflation"
No, there are circumstances in which the effects are non-Ricardian, and there are particular fiscal policies that will increase the inflation rate given the nominal interest rate. See: https://ideas.repec.org/a/eee/moneco/v73y2015icp70-92.html
But, that goes the other way. More government debt, in real terms, relaxes collateral constraints, the real rate rises, and inflation falls.
CA: "Also, if there exists a shortage in safe assets as in your models, wouldn't the government face a free lunch so long as demand for such assets is perfectly elastic and if the impact of the tax cut on income is sufficiently high?"Delete
Yes, that looks like a free lunch, in the sense that you can increase welfare. But, see the comment above.
Well, you could imagine a liquidity Premium linked to reserves that would make sure that they pay less interests than t bills (I know that's not the case in the real world).Delete
I am also thinking about helicopter drops. If the government finances a tax cut with reserves and reserves are perfect substitutes to t bills tan obviously this helicopter drop won't be different from a normal debt financed tax cut.
Things are different if the tax cut is financed with reserves that pay less tan t bills cause of a liquidity Premium. You can think of it as cash. If the tax cut is financed with cash and, for instance, some transaction can only be made with cash, so cash has a liquidity advantage, then I think the helicopter drop would cause inflation, in particular if the liquidity Premium on cash is decreasing in the quantity of cash.
Do you think that would not be the case?
"I know that's not the case in the real world"Delete
That's just it. At best, the central bank could issue a tradeable security - a Fed bill, for example (the Swiss National Bank has such an instrument), and that would be as liquid as a T bill. But, in reality reserves are not as liquid as T-bills. Only a subset of financial institutions can hold them. That's why the interest rate on reserves is higher than the T-bill rate.
I think the helicopter drop won't work to increase prices, even if it is a transfer financed by literally issuing currency. People have to be willing to hold the currency, but at existing prices and interest rates, they're not, and the outside money is held as reserves and doesn't affect inflation.
Stephen, why isn't this happening and what can make it happen? "If the Federal Reserve increases reserves, a single bank can make loans up to the amount of its excess reserves, creating an equal amount of deposits. The banking system, however, can create a multiple expansion of deposits. As each bank lends and creates a deposit, it loses reserves to other banks, which use them to increase their loans and thus create new deposits, until all excess reserves are used up."Delete
There is little interbank lending because the Fed pays interest on reserves. Shouldn't that be diminished or stopped? I don't like the idea of negative IOR because that could be passed on to retail bank accounts.
One more question, why are you not afraid of deflation, and of massively negative rates and even a cashless society? Or do those concern you? Thanks for your time.
1. I know the deposit creation story is popular in money and banking courses, but it's misleading. Banks are content to hold interest bearing reserves. They're not trying to get rid of the reserves by "loaning them out."Delete
2. The cost of negative interest rates is likely that it encourages too much currency to be held.
3. I was in Switzerland last fall, and no one there seems bothered by deflation.
1. Yes, but isn't that an argument for giving them nothing on reserves? You say, correctly that they don't want to lend, but isn't that part of the problem for our economy?Delete
2. People hoard currency for sure, when rates go negative. It is happening in Europe. But that is why that bank in Norway demanded the end of cash. That concerns me.
3. Deflation can get worse. Do central banks cause and control deflation or do they just stop it from getting too bad?
1. But lending is actually growing at a good rate.Delete
2. Banning cash won't solve any problems, and will create more.
3. Deflation isn't so bad. But you can see some of the costs - currency is too attractive. But the solution isn't to make cash less attractive by banning it.
Stephen, I really appreciate your patience.You are a Fed guy. You didn't give me a straight answer on how much control the Fed has over deflation and onthe intensity of deflation. Maybe you don't know. I would like to know if you know or if you don't know. I know the Fed mispriced risk in the past. That is a bubble blowing evil. A lot of people got hurt, especially in Las Vegas, where I live. Pets were abandoned, there were divorces, and lots of evil.The private foreign Fed is probably proud of all that, although I am not sure if you know.Delete
So,(to quote Janet Yellen), Is the Fed the cause of deflation? Well, not so far but soon?
And about Switzerland makes squat. They make snow and watches and they just charge more for both if their Frank balloons in value. Oh, and they do finance. What do they care about inflation or deflation? But what about people who make real ordinary things? Oh, and that chart of bank lending doesn't tell us who our banks are lending to. I bet it isn't much to Americans. Your opinion is valued but you can see that people in the real world are frustrated about all this. Thanks again for your time.
I'm trying hard to answer your questions, but it's difficult to figure out what you want to know. Yes, indeed, the Fed has control over deflation and inflation. They have promised 2% inflation, and if they don't deliver it, or something sufficiently close, you have something to complain about. To be more precise, here are the Fed's own stated goals:Delete
If you think they're not living up to that, or you think they should be doing something else, let someone know.
Thank you Stephen. I am just worried that the target of 2 percent could continue like the last crash with NGDP falling. I am shocked at the amount of lending the banks are doing (thanks for the FRED link), but I am thinking that they are lending to everyone but America. That doesn't seem to be helpful to our nation.Delete
You argue for the ne-Fisher effect and the importance of target interest rates. The Fed raised its target interest rate in December, but your 10-year breakeven inflation measure has fallen from around 1.5% to 1.18% in recent months. Exactly how long will it take for your neo-Fisher effect to kick in, as you say all monetary theory models except dumb ISLM/Phillips Curve ones forecast?
The Fed raised its target by 25 basis points in December. But, since then, according to whatever you might use to measure the views on what the Fed is likely to do, people are expecting that this will not continue. Fed funds futures prices seem to be telling us that the market thinks any more increases this year are unlikely. Thus the lower breakeven rates. So, this is entirely consistent with this post - it looks very neo-Fisherian. You can see in the 10-year bond yield chart that the U.S. yield is above those for Sweden and Japan. But, if the Fed does not continue raising its target, I would predict convergence to Japan.Delete
The 10 year tips spread also increased slightly in the week after the announcement.Delete
Not sure what you're getting at.Delete
Expected inflation rose in the short term after the announcement in December, which would be strange if raising the rate was going to decrease inflation.Delete
Stephen, somebody takes a look at your post here using an "off-the-shelf" Cash-In-Advance model, and concludes:ReplyDelete
"It's interesting that even this exceedingly simple monetary model fails to fully support the neo-Fisherian hypothesis."
The writer of the article seems quite confused. In fact, his model has a neo-fisherian effect. He himself says that when the nominal rate goes up future price levels are higher. Sure, current prices are not determined, but neo-fisherism does not say anything about current prices, it speaks about expected future inflation. Even if the current Price falls on impact, that's inflation today that falls, not expected inflation and neo-fisherism talks about expected inflation! It says that the peg is stable!Delete
Sorry, it doesn't fail there. Suppose R(t)=R forever. That pegs the inflation rate forever in your model - it's purely Fisherian. Of course, the price level at the beginning of time is proportional to the beginning-of-period money stock - the nominal interest rate has nothing to do with pegging that of course. But the first-period price level is irrelevant - that's just the neutrality of money at work (though of course in your model money is super neutral too). Think about another experiment. Set the first-period money stock at whatever you want. Fix R forever. Also, suppose that people in this economy have the option, at the beginning of each period, of putting their money in a reserve account earning R, instead of spending it. Let money grow at the constant rate from the first date commensurate with R as an equilibrium and no reserves held. Then at date T, sometime in the future, there is a level increase in M (fully anticipated), then M continues to grow at the previous rate. What happens?Delete
I agree that fixing the initial money supply would change the result and that the model is otherwise completely neo-Fisherian. Nevertheless, I think I may not have articulated my point correctly.
If a CIA model is going to have a neo-Fisherian result (which I will define as a nominal interest rate increase causing a corresponding increase in expected inflation that is not offset by current deflation -- hopefully this should deal with LM's complaint), then the current money supply must not fall.
If a central bank manages to increase the nominal interest rate by increasing the expected money supply, then the neo-Fisherian result as I previously defined holds.
I'm pretty sure that you don't usually make this reference to the money supply and only talk about the nominal interest rate by itself. This leaves the question of what happens to the money supply upon a rate increase open. If the mechanism for the rate increase is a fall in the current money supply instead of an increase in the future money supply, then the model fails to show the Neo-Fisherian result (as I defined).
I understand that, when money and government bonds are perfect substitutes, the money supply ceases to be relevant in CIA models. In this case, the effect of a rate increase would still be undefined -- did the central bank escape the 'liquidity trap' by decreasing the current money supply or increasing the future money supply?
Of course, increasing the future money supply is useless if the liquidity trap is expected to be permanent, so I was implicitly assuming that, when the central bank "increas[es] the future money supply," it is doing so at a point after the liquidity trap is no longer in effect and setting the money supply in each prior period sufficiently lower than its following money supply, such that expected inflation is above negative the rate of time preference.
If the central bank escapes the liquidity trap by reducing the current money supply, the model indeed does not support my definition of the neo-Fisherian result.
Sorry for the extremely long comment, I wanted to explain myself thoroughly.
"I'm pretty sure that you don't usually make this reference to the money supply and only talk about the nominal interest rate by itself."Delete
No. Of course, a central bank that is targeting a nominal interest rate has to support that policy with open market operations. In this case of this CIA, people often think of this as transfers - so it's whatever transfer policy supports the desired path for the nominal interest rate. This basic CIA is purely Fisherian - there's no liquidity effect in it. The real interest rate is constant.
"This basic CIA is purely Fisherian - there's no liquidity effect in it. The real interest rate is constant."Delete
I don't quite understand with your preoccupation with the liquidity effect as the primary way that models cease to exhibit neo-Fisherian qualities. I know you're anything but a fan of sticky prices (or any kind of nominal rigidity), but the most common way that the 'conventional wisdom' is brought about in the literature (that is, the price determinacy under interest rate rules literature) is through the addition of said friction.
Furthermore, and perhaps more importantly, if you assume that the central bank, instead of pegging the nominal interest rate, sets it according to an active Taylor Rule (plus some shock that it controls every period), then the neo-Fisherian nature of even simple cashless models (e.g., i = r + pi(+1), i = r + f(pi) + shock) becomes cloudy. In order to cause inflation to increase, now the central bank has to promise to have a lower interest rate, given the inflation rate.
So, if real world central banks do something closer to following an active Taylor Rule and setting a shock value each period than simply adjusting pegs, the correct policy response to low inflation is to promise lower rates given the rate of inflation. This appears to be what the Riksbank is trying to do, but maybe you are right and, rather than loosely following a monetary policy rule, they peg the nominal interest rate and change that peg on a whim. If that really is the case, then they should probably be raising rates, but I'm not quite sure.
"your preoccupation with the liquidity effect as the primary way that models cease to exhibit neo-Fisherian qualities."Delete
That's not a preoccupation. It's just definitional. You can separate the dynamic response to a change in the nominal interest rate into two components: (i) Fisher effect; (ii) liquidity effect. We know how the
Fisher effect works. The liquidity effect could be due to sticky prices, market segmentation, etc.
"In order to cause inflation to increase, now the central bank has to promise to have a lower interest rate, given the inflation rate."
Not correct: https://ideas.repec.org/a/eee/jetheo/v96y2001i1-2p40-69.html
The idea is: Show me your model, and I'll show you how it's neo-Fisherian. You can't sidestep the Fisher effect.
"...the correct policy response to low inflation is to promise lower rates given the rate of inflation. This appears to be what the Riksbank is trying to do..."
Exactly. Read "The Perils of Taylor Rules." We know what they're trying to do, and why. Given that they think that way, the theory says that they end up stuck in a low-inflation and low nominal interest rate steady state - assuming sticky prices, or not assuming sticky prices.
Here's my model, I assure you it exhibits the features I outlined above given my assumptions, feel free to test it yourself:Delete
Let's stick with the simplest model possible, the basic two equation cashless model from before:
(1) i_t = r + pi_t+1
(2) i_t = r + a pi_t + e_t
where i_t is the nominal interest rate, a > 1 is the coefficient on the Taylor Rule (I'm assuming active monetary policy here because I'd rather not deal with fiscal policy), pi_t is the current inflation rate, r is the constant real interest rate, and e_t is the shock variable that the central bank chooses each period.
The equilibrium for this model is pi_t+1 = a pi_t + e_t. If we ban explosive equilibria and the monetary policy shock is set to zero in each period, then pi_t = 0 for all t. What happens if e_0 is positive (consistent with the central bank setting a higher nominal interest rate for a given rate of inflation)? In this case, pi_1 = a pi_0 + e. Since we've banned explosive equilbria, we can simply solve backward from some period arbitrarily far in the future to get the equilibrium. In this case, I'll assume the economy is in equilibrium by t = 5. Given that and a value of zero for e in each period following t=0, pi_4, pi_3, pi_2, and pi_1 all equal zero. In this case, 0 = a pi_0 + e, or pi_0 = -(1/a)e. That is, for any positive value of e, pi_0 will be lower than it is in equilibrium. This is the point I made above and "The Perils of Taylor Rules" doesn't, to my knowledge, contradict it.
Of course, if I hadn't assumed active monetary policy and implicitly assumed passive fiscal policy, then the result would probably be different, but I honestly don't think the real world has active-fiscal passive-monetary (as defined by https://ideas.repec.org/a/eee/moneco/v27y1991i1p129-147.html) regimes all that often.
As I understand it, what "The Perils of Taylor Rules" points out is that the only stable equilibrium in a simple cashless model with a zero lower bound and an active Taylor Rule is the deflationary one. To my understanding the only way to escape this trap in that model is to increase the nominal interest rate, irrespective of inflation, but I'm also curious about the effectiveness of repeated negative shocks to a Taylor Rule (which would basically be equivalent to a higher inflation target) in this scenario. I haven't tested this, and maybe it's covered in the paper (which I will admit I have never fully read), but my intuition is that it might work.
You've almost got it. I think what you want to say is that e = (1-a)pi*, where pi* is the inflation target. In your model, the real rate is constant. It doesn't have to be a cashless model, as this works with, say, cash-in-advance and a constant endowment.Delete
Then, the two equations solve for a difference equation in pi_t,
pi_t+1 = api_t + (1-a)pi*
But you also want to take account of the lower bound on the nominal interest rate. Assume it's zero, so modify the above to get:
pi_t+1 = max[-r, api_t + (1-a)pi*]
There are two steady states: pi = pi*, and pi = -r. You solve the difference equation forward. Draw the picture and start with any initial condition and see what happens. If the initial condition is pi > pi*, that explodes and is not an equilibrium. But there is a continuum of equilibria with intital condition pi in [-r,pi*), and each of those equilibria converges to the zero lower bound. That's all for a > 1. But, if 0 < a < 1. Then, there are many equilibria that all converge to pi*. You can even have -1 < a < 0 (shocking!), and you get the same thing - all the equilibria converge to pi*. That is, under a Taylor rule for which the nominal interest rate goes down when inflation goes up, the steady state in which the CB hits its inflation target is stable.
What I was talking about was the effect of adding shocks to the model, I assumed the inflation target was zero. Adding an inflation target would produceDelete
pi_t+1 = a pi_t + (1-a)pi* + e_t
which, given e_x = 0 for all x > 0, would result in
pi_t = (1/a)((a-1)pi* - e_t)
The key question is what happens when e_t is positive. It turns out that a positive monetary policy shock causes inflation to fall; active Taylor Rules save the conventional wisdom as long as you ignore the zero lower bound and ban explosive solutions.
You're not solving this properly, as you can't ignore the zero lower bound (also what you're doing is technically incorrect). Conventionally, to study the behavior of stochastic models, people sometimes linearize around what they think is a stable steady state, or a unique deterministic equilibrium. Woodford would argue that the pi* equilibrium is unique, as he linearized a deterministic system and then argued that all the other potential equilibria are explosive - based on local behavior. But he's ignoring the global problem - that's the "perils of Taylor rules." The ZLB is actually stable. So, it would be natural to look at stochastic behavior in the neighborhood of the ZLB.Delete
You could make this easier. Forget about the Taylor rule, and just suppose in your equation (1) that i_t is stochastic. So, this implies thatDelete
i_t = r + E_t[pi_t+1]
So, when the nominal interest rate is high, expected inflation has to be high. Suppose that the nominal interest rate is first-order Markov, and is positively serially correlated. Then, states of the world with a high nominal interest rate have to be periods with a high inflation rate.
Many people are now talking about eliminating cash, citing terrorism, drugs etc as a rationale.
Do your models have anything to say about the desirability of this ?
Yes, in particular I've seen Rogoff's stuff on this, and heard him talk. I've haven't addressed this specifically (except in a tangential way), but this is an important question. In normal times, with essentially no reserves outstanding, most of the central bank's portfolio is financed with currency. But currency is aiding and abetting a host of undesirable activities. On the other hand, poor people use currency extensively in transactions. So, doing away with currency would hurt criminals, but it would also hurt poor people - there are distributional effects. Short of doing away with currency, we could tax it at a higher rate, i.e. have a higher inflation rate, but that is subject to the same problem. Doing away with large denominations (see Summers's blog post) has the advantage that it hurts criminals but doesn't hurt poor people. There are other solutions, including digital currencies. Green dot is a private (and apparently successful) alternative, probably used predominantly by poor people:Delete
Should central banks get into digital currencies? That's an open research question.