Why inflation will not fall off a bottomless cliff

"My model can identify the edge of a bottomless ZLB cliff. To the north of the edge of that cliff, there can be an equilibrium rate of inflation. To the south of the edge of that cliff, there cannot be an equilibrium rate of inflation, because the cliff is bottomless. Therefore inflation will not go south of that edge. We will never observe a truck going south over the edge of a bottomless cliff, because that can't be an equilibrium, since it is bottomless."

That's not good enough, but it's the best I can do. That is my reaction on reading Steve Williamson's post.

I have no (obvious major) problems with Steve's formal model. It is in Steve's interpretation of that formal model where I have a very big problem. If Steve had said 'This model shows that the central bank should not target a rate of inflation south of XYZ, because if it did so the inflation rate would fall over the edge of a bottomless cliff' I would be OK with it. But instead Steve is saying 'This model shows why inflation will not in fact go south of XYZ, because there is no equilibrium inflation rate over the edge of a bottomless cliff'.

This is not an isolated example. This is very much the same problem I have had with some of the things Narayana Kocherlakota has said. Something somewhere went very deeply wrong with the way macroeconomics is done in some places. I do not know why it went wrong like that.

This is not about politics or ideology. Explaining everything in terms of politics or ideology is one of those witchcraft explanations that only ignorant people use, who practice witchcraft themselves, and so think everyone else is a witch. I am pretty sure I am more right-wing than Steve is. This is about how we do economics.

This is not about sticky or flexible prices either. With sticky prices, the truck would fall slowly if it went over the edge of the cliff. With perfectly flexible prices it would fall instantly if it went over the edge of the cliff. But it could still fall over the edge of the cliff, regardless of whether prices are sticky or flexible (unless prices were completely stuck, of course, because then the truck can't move at all).

And it's not about who is more intelligent either. Steve probably is.

I despair of my ability to explain to Steve why I think his post is so horribly wrong. Why can't he just see it! It's obvious to my eyes. It's staring me straight in the face! All I can do is use useless metaphors about trucks not going over the edges of bottomless cliffs because the cliffs are bottomless.

Maybe I could suggest a minor change in his model. "Let's suppose there is a bottom to the cliff, because, oh, I don't know, the $20 note in my wallet would be worth more than the present value of the world's GDP, so I would buy the whole world, and live happily ever after, or something like that, so there is an equilibrium somewhere deep down there after all, so the truck can go over the edge of the cliff."

But that would be a total cop-out. His formal model is OK as is. It's telling us something interesting about the relationship between liquidity premia, time preference, and the location of the ZLB. It's his interpretation of that model that is so horribly wrong. It is not an explanation of why inflation did not in fact fall more than it did. How come he can't see it? How come there will be loads of other economists who won't see it either?

This is not just some random mistake on Steve's part. We all make those, and we can normally see them when other people point them out to us. This is not random; Steve is not alone; and I'm pretty sure he won't see it, and will just be bemused by this post.

What the hell has gone wrong with some of the best and brightest in economics? Is it too much math and not enough economics, so they are flying blind, reading the instruments, but have no idea what those instruments mean? Would it help to force them to say it in words? Or if they drew it in supply and demand curves, they would see that something is wrong. But we need math too, sometimes, because some things are hard to say clearly in words, or pictures. I despair.

Why didn't inflation fall further than it did when economies hit the ZLB? I don't know. Paul Krugman's explanation is that firms and workers don't like nominal wage cuts. Inflation fell over the edge of the cliff, but the cliff wasn't very deep at all. I think Paul's explanation is unsatisfactory and probably wrong. But it is an explanation. Steve's explanation isn't an explanation.

Update: there was significant deflation in the 1930's. It is not impossible.

Comments

[Ram]

You might say that he has a model in search of a theory. It's just a blog post, but if he's building a model prior to formulating a theory, he's putting the cart before the horse. Models formalize aspects of theories to derive non-obvious implications, to estimate theoretical quantities, to evaluate the theory against the data, etc. Without a theory, what purpose is the model serving? To be fair, Williamson thinks he has a theory, but the model seems to have come first.

[Geoffrey]

I'd be tempted to put it in mathematical terms. The idea is that if x determines y, and there is no x for which y is some value, then that value will never be reached. The mistake Williamson is making is that he's got it backwards, and is saying that x determines y, and because there is no y for which a certain value of x can be reached, then that value will never be reached. But y doesn't determine x, so that statement doesn't work.

To put it in your terms, the position of the truck determines the height. If there's no position for which the height is greater than Mt Everest, then we can say that the truck will never be higher than Mt Everest. But the height doesn't determine the position, so there's nothing wrong with a position who's height is indeterminate, because the height has no bearing on whether we end up at a certain position (unless we're steering the truck not to end up at an indeterminate height, but that IS letting height determine position).

[Nick Rowe]

Ram and Geoffrey: good comments. I don't have anything useful to add in response.

[Jacques René Giguère]

Or as Lerner said at Balaclava: "It's magnificent modeling but it's not science."

[Determinant]

Economics seems to have a strong liking for counter-intuitive conclusions. Perhaps in some cases it goes too far. Too much deduction and not enough skepticism, in other words.

[Peter N]

Krugman has Bewley in his corner.

http://econlog.econlib.org/archives/2013/09/why_dont_wages.html
http://cowles.econ.yale.edu/books/bewley/tfb_wages.htm

Part of the answer to wages not falling is that firms prefer layoffs. Those they hurt are no longer around to complain, and employers can lay off there least productive workers. General pay cuts tend to lose those who can most easily find a better paying job - the most productive.

In part time jobs and jobs with low autonomy, you do see wage cuts. There are obviously jobs where bad morale doesn't hurt productivity. There you also see wage cuts.

This effect does drive work to lower wage countries.

BTW I'd like to thank you for explaining the minimum wage. It's a Pigou tax on perceived undesirable labor practices. This is effectively the rationale used when it was passed.

"• eliminate labor standards that are so low they harm the ongoing efficiency, health, and well-being of workers.

• prevent unrestrained competition in labor markets from further lowering labor standards in affected industries, or spreading low standards to other industries.

• prevent low labor standards from interfering with attainment of full employment
and sustainable economic growth.

• eliminate low labor standards because they lead to labor disputes and divisive relations between employers and employees, thus further harming economic activity."

Whether these reasons are sufficient to justify a minimum wage is a different question, but the usual arguments don't directly address them.

In any case, in the recession we've seen the layoffs of high salary workers and the subsequent hiring of low salary workers. It's probably no coincidence that industries that pay low salaries are the ones that have done most of the hiring. It's mostly not a matter of direct replacement. This doesn't apply to part time workers where replacement has been direct.

It's also hard to have deflation when we've had rapidly rising net, a massive wave of refinancing, a return of consumer borrowing and corporate profits are exceptionally good, even if they come from lack of investment and lower staff levels.

Maybe we have Leijonhufvud's equilibrium of battling forces. I hope not.

[Jesse Huebsch]

My thought would be that there is no such thing as a static equilibrium in economics. The real world is always dynamic, and there can be dynamic equilibrium that look like static equilibrium with simple models, but only once the equilibrium is reached. This implies that using equilibrium conditions are only valid if the initial state is at equilibrium, or you can show that the dynamic system will converge to the equilibrium in question.
There is also a non equilibrium effect in the opposite dire, or hyper-inflation

[nemi]

"Something somewhere went very deeply wrong with the way macroeconomics is done in some places."

I still do not know why people tend to use this "macro" qualifier. I´m a micro economist, and as far as I can see macro is in a hundred times better state than micro. Macro is extremely hard - and while micro also is hard, most of the textbook stuff is simply incredible stupid.

And when it comes to the distinction between doing economics, even trivial economics, and extremely bizarre math - Oh my God, oh my God, oh my God.
I do not know how many times I have heard people claim stuff such as "the marginal costs (or benefits) differ between the actors - thus it is inefficient", referring to some general textbook conditions that should be fulfilled under certain circumstances - even though it is as clear as day that it would be inefficient to force such a solution in their particular model (because of e.g. technology or other constraints).

I have encountered the most mind numbingly stupid analogies between e.g. the trade offs between on the one hand hamburgers and broccoli and on the other health insurance and broccoli. Did you know that if you approve gov interference in one you also have to approve it in the other - don´t we, after all, have a totally preordered set of preferences over outcomes (which, in addition, does not even address market failures) - etc. etc. etc.

Is this the fault of economic theory or economists?
Well, what is the distinction? Is "the theory" something besides that which it communicates.

[JP Koning]

Hi Nick, glad to see I'm not the only one struggling with that post. You say that you understand his model. What do you think Steve means when he talks about a liquidity premium existing at the zero lower bound? Isn't one of the features of the zero lower bound (when the fed funds rate falls to zero) that the liquidity premium on money no longer exists?

[nemi]

PS: W.r.t. the theory and what it communicates:

Take, for example, how wages are determined in most textbooks. If we only look at the supply of labour, it is generally (always?) described as the firm having to set a wage that will make the marginal worker willing to forgo another hour of leisure - and is interpreted by everyone and his mother as a theory that gives a lot of agency/power to the worker (unlike in other social sciences).

Of course, another interpretation that would be equally consistent with the model would say that the wage a worker can demand is determined by that amount which would make another worker underbid him, and immediately would cause everyone to think of, if not Marxism, at least the reserve army of unemployed - and basically removes all agency/power from the worker.

Is the theory independent of how it is communicated? Hell no!!!!

[nemi]

PS 2: Sorry, forgot to make the point - which is that the math of course is the same irrespective of what words you put on the interpretation - and that is how ALWAYS, always, always, always how the one sided interpretations and framing (of which the above example is one of a million) been justified to me (and, I guess, anyone else who cared to ask).

That math rules, and interpretations is unimportant - is as far as I can tell a very integrated part of at least micro.

[nemi]

PS 3: Sorry - back again - even though I tried to concentrate on something different.

Anyway, to hear a mainstream (nothing bad implied) economist talk so directly about interpretations is just a bit much for my little brain to handle. If you actually think interpretations matter, and not just the math, and can convince one percent of economists of the same - economics could probably be revolutionized over night, even without any (big) change in core theories. It would give much less clear answers, and less guidance - but it would be wonderful.

[Adam P]

Hi Nick, it's been a long time.

I think the basic mistake Williamson makes is straightforward and typical of his mistakes (and the Kocherlakota one you recalled in the post).

He's only considering fully cleared markets and ignoring the possibility that some markets can fail to clear for years at a time.

Thus, Williamson fails to distinguish between the real rate the economy actually has and the "natural rate" which is the real rate the clears the labour market (really the natural rate clears the market for current goods and services but every model out there assumes a production technology that makes that the same thing).

So, for example, when Williamson says that raising the liquidity premium on government bonds lowers the real rate and raises inflation, both statements refer to market clearing values - it's none other than Krugman's old point about needing higher inflation to actually achieve a lower real rate when the natural rate has gone negative.

[Nick Rowe]

Jacques Rene: well, I would say it's good modelling, but he's not modelling what he thinks he's modelling.

Determinant: yep, economists get a kick out of building models with surprising results. But when we do that, we normally say "Hey! Look at this! Isn't my result surprising!" And then we (try to) explain the intuition why we get our surprising results, and why everyone else getting the old boring results is wrong. For example, my post on optimal fiscal policy in hybrid OK/NK models.

Peter N: "Part of the answer to wages not falling is that firms prefer layoffs."

But it should be *real* wages not nominal wages, not falling.

On minimum wages:

1. a price floor is not the same as a tax unless you specify the rationing mechanism of a price floor.
2. I would be surprised if those who support the minimum wage would be very happy to replace it with a Pigou tax on low-wage workers.
3. You are off-topic and trolling. Stop.

[Nick Rowe]

Jesse: I think that's right. We could talk about dynamic equilibria, or we could talk about stability, but I think we would end up in roughly the same place.

JP: see my reply to Adam P below.

nemi: well, we normally talk about (e.g.) both the supply and the demand for labour. And how there is only one W* at which Ls=Ld. And how if W < W* it would be in the interest of an individual firm to offer a slightly higher W than all the other firms, and how if W > W* it would be in the interest of an individual firm to offer a slightly lower W than all the other firms. But if I drew a vertical supply and demand curve, on top of each other, and the demand curve suddenly curved the wrong way at Wzlb, so there would be an excess *supply* of labour if W < Wzlb, and then said: "this explains why W will not fall below Wzlb", most people would see the problem with my model.

"If you actually think interpretations matter, and not just the math, and can convince one percent of economists of the same..."

I think a large percentage of economists wouldn't need any convincing.

Adam P.: WELCOME BACK!!!

"So, for example, when Williamson says that raising the liquidity premium on government bonds lowers the real rate and raises inflation, both statements refer to market clearing values - it's none other than Krugman's old point about needing higher inflation to actually achieve a lower real rate when the natural rate has gone negative."

Yes!

What Steve is adding (when we interpret him this way), is that the natural rate on (say) bonds, will equal the rate of time preference (given his assumption of stationary economy, which is OK to simplify) minus the liquidity premium on bonds. So, for a given rate of time preference, the higher the liquidity premium on bonds, the higher the target rate of inflation would need to be to avoid the ZLB. Which is a useful point to make.

We cannot talk about *the* natural rate, in a world where different assets differ in liquidity, because each asset will have its own natural rate. And (JP) the liquidity premium on money over bonds, at the margin, will be be a decreasing function of M/P, but it may or may not asymptote to zero. In the olden days, we would sometimes draw a horizontal LM curve for the liquidity trap at a nominal interest rate strictly above 0% (on bonds). Steve is saying what we used to say in the olden days when we did that. We used to distinguish between a liquidity trap, and an *absolute* liquidity trap, where "absolute" meant 0% nominal on bonds, which is what we nowadays call the ZLB. The Old Keynesians were here first, in their own funny way.

[Adam P]

Yes, I agree with everything you just said.

In particular "for a given rate of time preference, the higher the liquidity premium on bonds, the higher the target rate of inflation would need to be to avoid the ZLB". Isn't that the greatest irony ever? SW is giving theoretical support to one of Krugman's core positions, which is why I doubt he'll be happy being interpreted that way!

If we don't interpret him that way then it gets hard to give him credit for making any sense, as you allude to in the post. For example, in the paper (of his) that he links to he says that the reason QE lowers inflation is that when the supply of reserves is increased their real return must increase so they'll be held. This directly implies that when increasing the supply of reserves if the fed doesn't want inflation to fall it need only increase the IOER.

Again, you raise rates to raise inflation... I think we heard this before, I don't recall we thought it made sense.

[David Andolfatto]

Honestly, Nick, I have no idea what you're on about here.

The theoretical context in which Steve is framing his discussion is clear. We know he is using the rational expectations solution concept, and he explicitly states that he is considering a case where any nominal rigidities have worked themselves out. And yes, he assumes market-clearing (and stationarity).

The analysis he presents in his post is nothing more than glorified "Fisher equations" -- no-arbitrage-conditions that arguably must hold (try arguing otherwise). There is not enough structure in the post to determine the assumed direction of causality -- he speaks as if liquidity premia are exogenous and determine other variables (via the no-arbitrage-conditions). But if you go read his papers, you will see that it is the outstanding stock of "liquid" assets (including government money and bonds) that is exogenous. If these liquid assets are in "short supply," then liquidity premia emerge and the effects Steve talks about hold true (in the context of the model - of course, there are other assumptions about policy, but these are details.)

In Steve's model, it is possible to have an "asset shortage" (liquidity premia) even when the nominal interest rate is zero. If money and bonds are perfect substitutes, you get the classic "liquidity trap" effect of an OMO. But Steve has another model where money and bonds are not perfect substitutes (and where the fiscal authority behaves suboptimally.) QE in that context (sucking out less liquid debt and replacing it with liquid assets) reduces liquidity premia. Ceteris paribus, the model suggests that this must lead to lower inflation.

You can argue till you're blue in the face about "interpretations," but to my eye, the model's predictions and Steve's interpretation of these predictions does not seem inconsistent with the data. And ultimately, this is how Steve's model (or any model) will (should) be judged.

[nemi]

Nick; Yes, the mathematical structure is the same. If you estimated the demand and supply it would be the same. You would get the same W. If your only aim were to know how W would change with respect to a shift in the demand curve - if it were a pure technical question, they would be the same. That is the mathematics of it. BUT, clearly, it is two radically different theories. Clearly, there would be a gigantic difference in attitude between those who learned from the first and second formulation.

"And how if W < W* it would be in the interest of an individual firm to offer a slightly higher W than all the other firms, and how if W > W* it would be in the interest of an individual firm to offer a slightly lower W than all the other firms."

Yes, it is described as the firm having to groom the workers - rather than the firm being able to pit the different workers against each other. Big big big difference. Neither of the theories is right or wrong, even if we assume that the mathematical structure of the relationships is right - they are simply different perspectives. Most ideologies, except utilitarianism, is simply a play of words - so clearly it creates differences in opinion, as well as factual assessments (see e.g. the difference in opinions between economists in different countries but who all use the same models).

When I read your answer, not only do I not think most economist disagree with me, it does not even seem like you agree with me (I got kind of exited there for a moment).
When I reread your post I see that your argument with Williamson is purely technical - and I guess that you can call that "interpretation" to - but I usually use it in order to refer to the assignment of meaning with correct argumentation taken as a given.

[Majromax]

> given his assumption of stationary economy, which is OK to simplify

My apologies for the 101, but is this really an OK simplification when we're looking at interest and inflation rates? I think there may be a contradiction earlier in the model specification:

> A ubiquitous result is the Friedman rule, which says that an optimal monetary policy eliminates inefficiency by reducing L(t) to zero, which implies a zero nominal interest rate, i.e. q(t)=1. Then, supposing an equilibrium in which consumption is constant over time, (1) and (2) give [deflation equal to the discount factor]

But if we're assuming that consumption is constant over time, then I don't see any reason to assume that there is a non-unity discount factor for the economy in aggregate, and consequently no need for a deflationary equilibrium even before we talk about the ZLB.

Let's make this a bit more concrete with an overlapping generations model; a fixed number of agents individually have greater-than-unity discount factor, such that they want to consume B/2 > 0.5 of their total consumption in the "young" phase and (1-B/2) < 0.5 of their total consumption in the "old" phase. Further assume a zero nominal interest rate and full price flexibility, such that the always-constant output is purchased for all currency used during a period.

Now, let's look at stability and add inflation to the mix. We'll assume a sequence: agents make decisions on spending mix in advance, (inflated) wages are distributed, then spending happens and we see what the clearing price level is. If inflation is totally unexpected, then the nominal spending in a period is (1+p')*(B/2) [wages] + (1-B/2) [spent savings], giving a total NGDP of 1+p'*B/2, or a post-facto inflation rate of p'*B/2. Provided agents never adjust their spending mix, this means that an inflation shock will dampen out over time (as |p'*B/2| < |p'|).

Adding in expected inflation, an agent expecting inflation of p* will seek to consume (C) such that B/(2-B) = (1+p*)C/(1-C), giving C=B/(2+p*-Bp*). The total spendings in a period will then be (1+p')*C+(1-C) = 1 + p'*C. This is still stabilizing provided C<1, which will always be the case (as C represents the consumed fraction of income).

So with no nominal interest and a fixed output, even if each individual agent in an OLG model has a time preference the economy as a whole still behaves like it is time indifferent. Further, the OLG model indicates that inflation damps out over time to a zero rate, even if agents attempt to anticipate a constant, nonzero level. (Maybe there's a higher-order instability if agents anticipate alternating inflation and deflation?)

[Jacques René Giguère]

My one cent worth.David Andolfato beat me to it. Like everyone I teach my students the usual:that a model must first be internally logically and mathematically consistent( only a few cranks fail this) and then you move to the empirical tests (the twin contradictory of compactness and completeness) but the real one is correspondence.
Stephen will live or die by the data though I am much less confident than David that Stephen will be vindicated.

[Mark A. Sadowski]

"Stephen will live or die by the data though I am much less confident than David that Stephen will be vindicated."

Stephen's model predicts QE lowers nominal rates and lowers the rate of inflation. And yet there is empirical evidence that neither is true.

For example, take Japan in 2001-2006.

In “An Injection of Base Money at Zero Interest Rates: Empirical Evidence from the Japanese Experience 2001–2006" by Yuzo Honda, Yoshihiro Kuroki, and Minoru Tachibana (March 2007):

http://www2.econ.osaka-u.ac.jp/library/global/dp/0708.pdf

Figure 3 shows that Honda et al finds the original Japanese QE raised the yields of 5, 7 and 10 year bonds by statistically significant amounts. Table 2 shows that reserve balances Granger caused core CPI (and to be clear, the effect is positive).

Or, for example, take the US since 2008.

QE1 was announced on November 25, 2008 and concluded on March 31, 2010. The 10-year T-Note closed at 3.35% on November 24, 2008 and closed at 3.84% on March 31, 2010, an increase of 49 basis points.

QE2 was hinted at in Jackson Hole on August 27, 2010 and concluded on June 30, 2011. The 10-year T-Note closed at 2.50% on August 26, 2010 and closed at 3.18% on June 30, 2011, an increase of 68 basis points.

QE3 was hinted at in Jackson Hole on August 31, 2012. The 10-year T-Note closed at 1.63% on August 30, 2012 and 2.71% on November 26, 2013, an increase of 108 basis points.

http://1.bp.blogspot.com/-BAnvd5XkIkc/UnKFj667RyI/AAAAAAAAAyM/-xbQBsjqcm0/s1600/QE+Rates.png

I've run Granger causality tests using the Toda and Yamamato technique on the US monetary base since December 2008, and find the monetary base Granger causes 10-year T-Note yields and the PCEPI and the impulse responses are positive in each case. Furthermore, I've estimated a VAR similar to Honda et al for the US over the period since December 2008 using industrial production, the PCEPI, the monetary base and the 10-year T-Note as variables, and find the impulse response of PCEPI and the 10-year T-Note yields to the monetary base are both significantly positive.

Stephen's model is interesting, but in my opinion it simply doesn't match the empirical facts.

[Jacques René Giguère]

Mark: not being a high-level macro guy but a more down to earth industrial organisation college type, I try to keep my public judments on a more ambivalent level. But I agree with you.

[stearm]

My five cents: we know that the best way to create inflation is to print money and find the best way to make money circulate and eventually increase the velocity of circulation and also Y. And we also know that QE is failing to create inflation. So clearly QE is far from being the best way to create money out of the blue and stimulate the economy under current conditions.

But, then, Williamson arrives and says that, if we only stop QE, then inflation will re-appear. He fells short from say that QE led us at the ZLB by causing an event that happened before QE was implemented, but ok, he still has a reputation to defend outside his ideological circle of friend.

It's like when you have to take a medicine, but you choose another one containing 5% of the active principle and 95% a placebo substance. You don't die, but don't recover either. Then, Williamson arrives with a model that says, look what you take won't eliminate the disease. And he is right, but then add: "stop taking that medicine and you will be fine".

Immaculate healing!

Have you an idea why Williamson can't say: take the real medicine and you'll be fine?

By the way, the kind of math economists like Williamson and many others (NK included) is useless in economics. But as an ideological tool it deserves a lot of respect.

Adieu.

[Robert Waldmann]

OK so I'm a leftist and deeply disagree with Williamson's view of what economic science is and what it should be, so I have nothing useful to contribute. But that never stopped me before. It seems clear that the problem is the assumption that the scaled economy must reach a steady state. Here I note that standard macro (new Keynesian but also RBC) includes a unstated methodological a priori that real variables will converge to The balanced growth path (steady state of the scaled economy). It is also standard to assume that, without exogenous shocks, the economy will converge on The saddle path.

These assumptions absolutely do not follow from assumptions of rationality or from assumptions about tastes and technology which economists consider reasonable for some other reason. They are required to obtain predictions (with indeterminate equilibrium it is not possible to deduce the effects of policies) and for computeres to be able to approximately calculate those predictions. It is so standard to assume we have a can opener, that macroeconomists forget that one of there assumptions is that the scaled economy reaches a stready state.

Williamson abandons the full standard assume everything really important by presenting a model with 2 steady states. But he assumes that one must be reached. The fact that assumptions are essentially always made so analysis can be local to the steady state seems to have causec Williamson to skip the step of making sure he has assumed whatever he has to assume to keep the economy close to the low inflation steady state.

I think that the problem is that macro theorists always cheat and forget that they have been cheating and assume that the familiar results are not the result of assuming the familiar results and back engineering assumptions.

I have other thoughts. One os that the ambiguity of "equilibrium" is part of the problem. It is standard to assume that the world is in Nash equilibrium. This does not mean it has a stable teady state. The original use of the word "equilibrium" by economists was as "stable steady state". This is still the way the word is used in the natural sciences. I think part of the mistake is the erroneous logic " we assume Nash equilibrium even though it is grossly implausible, so we just assume equilibrium so we just assume no boundless deflation.

Finally Euler equations allow many apparent solutions which aren't solutions at all, because they violate the transversality condition. The idea that apparent solutions which go off somewhere crazy are't solutions can be missapplied to models in whose dynamics are not a Euler equation (or maybe it would be clearer if I said not asset value equations). thus your no buying the world ith a 20 is the missing assumption which rules out unbounded deflation. But the Pigou effect will create a 3rd dimension. Your corrected model can't be illustrated with a 2 dimensional graph.

I think I'm back to the guess that Williamson assumes that Nash equilibria which don't converge to a steady state are always ruled out, and forgot that this requires finding a sufficient assumption to rule them out and then claiming to find it reasonable and then solving the new model which has been reverse engineered to give the desired result. Your additional assumption actually is reasonable, but it is part of a model quite different from his.

[The Keystone Garter]

Pre-WWII, banks in North America turned off the credit taps. With what people know about banking, if banks turned off the taps again, after a certain point, people would revolt and install their own banks that lent. There are other ways for deflation to occur than under the collapse of fractional banking. I view the point of central banks as to inflate where a nation is poised to responsibly surveil WMDs, and deflate where doing the converse; the human capital is hard to measure. I don't think the CPI analogy is appropriate. There is a ratio of two CPIs. A desirable one and one that represents WMDs and tyrannic dystopias. My model says if everyone is being bad, everyone should deflate. But that would presumably lead to revolution, assuming the Senate and other checks on power are compromised. Like in Germany, too much deflation incurs unpredictable emotional consequences. It helps to have a population that doesn't have a chip on their shoulders, to incur deflation responsibly.
Risking deflation is an experiment no one wants to run. We should make Iceland run it.

[Jeremy Fox]

All I wanted to say is that as an ecologist it's a very weird experience to look in on this discussion. I don't have the expertise to comment on the model under discussion--but the fact that the people who do have the relevant expertise would even need to *have* this discussion is totally foreign to me. I just can't imagine there ever being any doubt in ecology as to whether someone had fully specified their dynamical model. Or trying to analyze a model by just looking at where the equilibria fall in phase space as a function of the model parameters, without looking at the stability of those equilibria. Or finding that their assumptions imply strange or unrealistic dynamics (e.g., no stable equilibria or whatever), and "fixing" this problem by simply *assuming* that the strange or unrealistic dynamics don't occur (I hadn't realized the old "assume a can opener" joke might actually have truth to it!)

And dynamical models in ecology quite often include assumptions that the organisms concerned behave adaptively or even optimally, so the difference isn't that ecologists are only looking at models lacking any notion of optimality or rationality or whatever...

[Jeremy Fox]

In case you didn't notice Ben J, the *economist* who wrote this post and several of the *economists* commenting on it share my worry. Are they condescending too?

Nothing I said implies that I think macroeconomists are dumb (they're not; they're smart), or incompetent (they're not), or that they're not as smart as scientists (I'm sure they're just as smart), or that macroeconomic math is easy (it's not, it's hard; in fact I bet it's probably harder than at least much of the math that gets used in mainstream ecology), or that scientists never make mistakes (they make plenty, both technical ones and other sorts).

In my comment, I expressed surprise not that some macroeconomists might be making mistakes (after all, macroeconomics is difficult), but at the particular kind of mistake they might be making here. I'm surprised because it's quite different from the sort of mistake that gets made in my own field (including by me, in case you were thinking of accusing me of condescending to everyone, ecologists and macroeconomists alike). I suspect that, were macroeconomists to look at my own field, they too would be bemused at some of the mistakes that get made and the issues that get debated.

I do think that if the particular kind of mistake discussed in this post is actually getting made, then that might suggest a need for macroeconomists to rethink their modeling approach and/or the way they train their students. But that's a very tentative suggestion, given my limited knowledge of macroeconomic models and how they're taught.

In case you still think I'm condescending about economists, please read the following posts on my blog. I find the analogies between economics and ecology interesting and often draw on my admittedly-very-limited knowledge of economics in my own writing.

http://dynamicecology.wordpress.com/2013/10/22/measuring-resource-competition-vs-measuring-inflation/
http://dynamicecology.wordpress.com/2013/05/06/we-need-more-short-selling-of-scientific-ideas/
http://dynamicecology.wordpress.com/2012/08/29/what-evolutionary-biology-looks-like-to-an-economist/

Finally, I've met Nick and have a lot of respect for him; I would never condescend to him or his macroeconomic colleagues.

I trust this clarifies my earlier comment.

[Nick Rowe]

David: "Honestly, Nick, I have no idea what you're on about here."

That is what I feared. I think Steve would have the same reaction. But notice that Adam P, for example, understands exactly what I'm on about, and Adam, like us, has a Phd from a good school.

Let me try it this way:

Suppose the central bank sets the money supply. Assume perfectly flexible prices and rational expectations.

1. If the central bank increases the growth rate of the money supply, the inflation rate will rise by the same amount, and so will the nominal interest rate. Standard Fisher Equation result. But Steve has identified a minimum equilibrium rate of inflation, call it zlb. And associated with that zlb rate of inflation, there must be a growth rate of the money supply (the same zlb, assuming the economy is stationary). ***What happens if the central bank drops the growth rate of the money supply below that rate zlb?*** Would Steve (or you) say that cannot happen? But it *can* happen. If the printing press breaks down, or if some notes get lost, it *will* happen. What then? Can't inflation drop below Steve's minimum zlb level? It must, and if it does so, then Steve's equation 1(?) will be violated, and markets will not clear. There will be an excess demand for money, and excess supply of goods, and inflation will fall without limit.

2. If the central bank increases the money growth rate that will cause an increase in the inflation rate and an increase in the nominal interest rate. But we cannot reverse causality and say that if the central bank increases the nominal interest rate that will cause the inflation rate to rise. Sometimes we cannot reverse causality statements. If I press down on the gas pedal, the speedometer needle will rotate clockwise. But if I grab hold of the speedometer needle, and rotate it clockwise, that does not cause the gas pedal to go down.

3. For 20 years (and more) the Bank of Canada (and others) has followed this procedure: if inflation looks like it's heading below 2%, *lower* the nominal interest rate to increase inflation; if the inflation rate looks like it's heading above 2%, *raise* the nominal interest rate to decrease inflation. Are you saying the Bank of Canada has been turning the steering wheel the wrong way? If so, it must have been a miracle that inflation averaged almost exactly 2% over the last 20 years. Because if a bus driver thinks you need to turn the steering wheel clockwise to make the bus turn left, he would almost certainly start veering off course almost immediately, and just run in circles.

[Nick Rowe]

Robert: I tried to leave this comment on Brad DeLong's recent blog post, in response to him and to your comment there. But it seems I have to have a Facebook account or something to comment there, so I failed:

"I'm pretty sure I would fail badly an exam on Franklin Fisher. I'm at the kindergarten level: if I see a supply and demand curve cross the wrong way, I get worried about stability.

But is stability of *Walrasian* general equilibrium what we should be interested in? We don't have one big market in which n goods are traded. We have n-1 markets, in each of which one of the n-1 goods is traded against the nth good -- money. And the stability of equilibrium in a monetary exchange economy strikes me as being a fundamentally different question from the stability of equilibrium in a Walrasian economy. Moreover, stability of equilibrium in which trading at disequilibrium prices leads to rationing, so we are talking about stability when prices adjust to excess *constrained* demands -- as opposed to excess *notional* demands -- strikes me as being a fundamentally different question again.

I vaguely remember back in grad skool Peter Howitt saying that Dreze(?) had proved stability in a monetary exchange economy when *money* prices respond to excess *constrained* demands. But I can't remember necessary or sufficient conditions. Does that ring any bells with you or Robert?

In the olden days we also used to worry about stability of Nash equilibrium. We would draw cobweb patterns around the reaction functions, and see if it converged. Nowadays I think they just assume the players jump straight to the Nash equilibrium, and think the cobwebs are silly. But if each player does not know where the other players' reaction functions are located, it doesn't sound so silly to me."

[Nick Rowe]

Mark: "Stephen's model is interesting, but in my opinion it simply doesn't match the empirical facts."

Stephen's model is not (IMO) even a model of the *actual* rate of inflation. It is a model of the *mimimum desirable* rate of inflation. If I thought that Stephen's model did fit the empirical facts, I would conclude that there must be an omniscient truck driver somewhere, either in the central bank or up in heaven, who liked to drive as close to the edge of the cliff as possible, without actually going over the cliff.

[Nick Rowe]

Jeremy: your comment was both sensible and respectful. I had already unpublished Ben J's comment.

(I have also unpublished Peter N's comment, which ignored my repeated warnings about trolling and going off-topic.)

[Ben J]

Apologies to Jeremy and Nick! Obviously I am too sensitive. Thanks for clarifying Jeremy.

[PeterN]

I was replying to this

"Paul Krugman's explanation is that firms and workers don't like nominal wage cuts. Inflation fell over the edge of the cliff, but the cliff wasn't very deep at all. I think Paul's explanation is unsatisfactory and probably wrong. But it is an explanation."

and

"Peter N: "Part of the answer to wages not falling is that firms prefer layoffs."

But it should be *real* wages not nominal wages, not falling."

This is off topic because???

If you're mad, take it out on DeLong.

[Rajiv Sethi]

"Would it help to force them to say it in words?"

It would help immensely. This is why it was a lot easier to see the error in Kocherlakota's claim that "if the FOMC maintains the fed funds rate at its current level of 0-25 basis points for too long, both anticipated and actual inflation have to become negative... over the long run, a low fed funds rate must lead to consistent—but low—levels of deflation." I suspect that something similar may be going on here, and that Stephen is doing comparative statics on an equilibrium that is locally unstable under learning. But Stephen (in a comment on his blog) denies that this has anything to do with stability, and is working on a rebuttal. And he earlier argued that Kocherlakota's claim was innocuous.

I will just point out, again, the usefulness of considering disequilibrium dynamics when one obtains counter-intuitive comparative statics results. In Kocherlakota's case I found Peter Howitt's 1992 JPE paper very useful:

http://rajivsethi.blogspot.com/2010/08/lessons-from-kocherlakota-controversy.html

Could the recent changes at the Minneapolis Fed have something to to with Narayana's reassessment of the usefulness of these models?

[Barry]

Nick: "What the hell has gone wrong with some of the best and brightest in economics? Is it too much math and not enough economics, so they are flying blind, reading the instruments, but have no idea what those instruments mean? Would it help to force them to say it in words? Or if they drew it in supply and demand curves, they would see that something is wrong. But we need math too, sometimes, because some things are hard to say clearly in words, or pictures. I despair."

Nick. From what I uunderstand, Stephen was and is one ofthe people warning about high/hyper inflation, and hasn't let facts contradict his theories. Also, I've seen his comments on various blogs, which I'd rate as vaccuous.

Whar has he actually done to deserve a 'best and brightest' title, and why doesn't macro understand the concept of 'has been'?

For example, the dirings at the Minn Fed are well -explained as two grotesquely wrong 'experts' getting the well-deserved boot after years of being wrong and refusing to change. The only anomaly is that right-wing 'experts' rarely suffer from being wrong, when their errors serve the elites.

[Barry]

Sorry for the typos; it's hard to write full paragraphs on an iPad.

[Nick Rowe]

Rajiv: With the Kocherlakota question, it was very much about stability. But I'm not sure it is just about stability in this case. Let me try this:

I could easily imagine you or I writing down (something like) Stephen's equations and inequalities, and saying: "we must ensure that inflation satisfies those equations and inequalities otherwise there will not exist a full-employment equilibrium". We would be making a *normative* statement about policy, and about what we *want* to happen in the world. I read Stephen as saying: "This equilibrium must exist, and we must be in this equilibrium, and therefore this explains what is in fact happening with inflation." He is making a *positive* statement about the world based on the assumption we must be in that equilibrium.

It's more about existence than stability. It's switching positive statements for normative policy recommendations. It is as if he said: "it is impossible for the money supply growth rate to be negative (or more negative than xyz), because if it were negative there wouldn't exist a market-clearing equilibrium".

Barry: " The only anomaly is that right-wing 'experts' rarely suffer from being wrong, when their errors serve the elites."

Oh God. Once again, this is not about politics. That is the sort of response that knuckle-dragging ideologues assume about everything they don't understand and don't like: "they must be witches!" If I wanted to hire someone to serve the elite, these guys would not be anywhere on my list. They aren't even properly right-wing, they are far too nerdy and out of it to be any sort of wing. An equilibrium could be a good or bad equilibrium. And an equilibrium with the government doing XZY could be better or worse than one without the government doing XYZ.

[Nick Rowe]

In fact, if I were a crazed lefty, who wanted to destroy the market economy and bring forward the revolution, I would put guys like this in charge of monetary policy. Hmmmm. I bet Minnesota is really a commie plot!

[Nick Rowe]

Why don't printing presses break down more often?

Many engineers and maintenance workers have recently been puzzled by the recent reliability of certain printing presses. Specifically, those printing presses that central banks use to print money. Why don't they break down more often?

My Minnesota co-author and I have been working on a simple economic model to explain this puzzle. Here is a rough sketch of our model:

There is a real rate of interest consistent with output remaining at potential, call it r*. We show that r* depends on preferences and the growth rate of potential output.

Given r*, and the liquidity of various assets, there exists a minimum rate of inflation, call it Pdotmin, consistent with our model's equilibrium. We know that the actual inflation rate, Pdot, must be greater than or equal to Pdotmin.

Given Pdotmin, the growth rate of potential output, and the money demand function, there exists a minimum growth rate of the money supply, call it Mdotmin, consistent with our model's equilibrium. The actual growth rate of the money supply, Mdot, must be greater than or equal to Mdotmin.

Recent events have caused an increase in liquidity premiums, which our model says would increase Mdotmin.

Since Mdot >= Mdotmin has recently been a binding constraint, this increase in liquidity premiums has therefore caused printing presses to be more reliable than they would normally be.

It would have been impossible for printing presses to have broken down more often than they did, because that would have meant that equilibrium in our model did not exist.

[Adam P]

Nick, mate you've got Delong and Krugman seriously worried about your health!

On lots of things I'd take those guys pretty seriously, should I be worried? It's ok to admit it.

Anyway, you're actually on to a really important point in a comment above that I think really needs a full post:

"I could easily imagine you or I writing down (something like) Stephen's equations and inequalities, and saying: "we must ensure that inflation satisfies those equations and inequalities otherwise there will not exist a full-employment equilibrium". We would be making a *normative* statement about policy, and about what we *want* to happen in the world. I read Stephen as saying: "This equilibrium must exist, and we must be in this equilibrium, and therefore this explains what is in fact happening with inflation." He is making a *positive* statement about the world based on the assumption we must be in that equilibrium.

It's more about existence than stability. It's switching positive statements for normative policy recommendations. It is as if he said: "it is impossible for the money supply growth rate to be negative (or more negative than xyz), because if it were negative there wouldn't exist a market-clearing equilibrium"."

This is a form of cheap bait and switch that Williamson pretty much always engages in, as does Andolfatto in his weak attempts to defend SW.

Notice how SW's post reads, for most if it the statements have the form "in my model QE works but not as the (real world) Fed thinks it does", "in my model this could lead to a deflationary trap", "in my model...".

Then, in his last two paragraphs SW switches to statements of the form "the Fed is in a trap...".

Andolfatto defends by talking entirely in the context of the model, as if SW just gave a counter-example to someone else's claim and so the validity of the example only depends on it's own internal consistency. I recall you giving a counter-example to a Krugman claim on debt burdens, recall that you didn't need to argue about who's framework was more relevant to the real world (OLG or dynastic agents) because he made an unqualified claim and it was a counter-example. (We can ignore the fact that even in this Andolfatto is wrong as the discussion of dynamics on Krugman's blog makes clear.)

The point, and the reason this needs you to do a post, is that SW is doing something potentially very pernicious here (if anyone listens to him). He appears to keep his academic detachment the whole way with the "in my model..." qualifiers and then switches to positive statements about what the Fed is actually doing and why this is dangerous and the FOMC are idiots.

An average reader won't understand the theory that deeply and will trust SW to make the correct conclusions and that might lead them to think the Fed is doing them great potential harm when the exact opposite is true.

[David Andolfatto]

Adam P,

I find it interesting how we can read the same post and come to very different impressions of what Steve is suggesting in the way of policy. He is saying that *if* the problem is an asset shortage, then there's really not much the Fed can do about it. Maybe tinker around a bit with asset swaps (an effect that may have some surprising implications for inflation). But the real solution is a short term increase in Treasury debt -- something beyond the power of the Fed to accomplish. This is a policy recommendation that I'm sure Krugman and DeLong would favor. The fact that they (and you, and Nick, and most others) did not catch it demonstrates that you nobody really bothered reading Steve's papers before joyfully portraying him as an ignoramus.

By the way, exactly where does Steve say that what the Fed is doing is "dangerous" and that the FOMC are "idiots"? It seems to me that you are putting words in his mouth.

[Adam P]

David,

I did notice that implication but ignored it in concentrate on this part:

"But that's not the way the Fed is thinking about the problem. What I hear coming out of the mouths of some Fed officials is that: (i) Things are bad in the labor market, and the Fed can do something about that; (ii) inflation is low. Thus, according to various Fed officials, the Fed can kill two birds with one stone, so it should: (a) keep doing QE; (ii) make it clear that it wants to keep the interest rate on reserves at 0.25% for a very long period of time.

What I hope the discussion above makes clear is that this is a trap for the Fed. There is not much that the Fed can do on its own about the short supply of liquid assets. They can get some action from QE, but the matter is mostly out of their hands, and more QE actually pushes the Fed further from its inflation goal. If the Fed actually wants more inflation, the nominal interest rate on reserves will have to go up. Of course that will lead to some short-term negative effects because of money nonneutralities.

The Fed is stuck. It is committed to a future path for policy, and going back on that policy would require that people at the top absorb some new ideas, and maybe eat some crow. Not likely to happen. The observation of continued low, or falling, inflation will only confirm the Fed's belief that it is not doing enough, not committed to doing that for a long enough time, or not being convincing enough"

Notice in the second middle paragraph SW says "What I hope the discussion above makes clear is that this is a trap for the Fed. There is not much that the Fed can do on its own about the short supply of liquid assets."

Where's the "if" type qualifier, that's his summation and the switch has been made. The rest is just small minded scaremongering, a bit pathetic but still someone might take it seriously.

[David Andolfatto]

Nick:

"That is what I feared. I think Steve would have the same reaction. But notice that Adam P, for example, understands exactly what I'm on about, and Adam, like us, has a Phd from a good school."

So you are saying that Adam is just as confused as you are. ;)

Nick, you misunderstood me. I'm pretty sure what you say makes sense in the context of *some* theory. What I didn't get was how you quickly piled on Steve (motivating others to do likewise), without understanding his specific model (admit it, you did not go read his paper). There may indeed be a lot of things not to like about Steve's paper, but this is where we debate the substance of the ideas put forward. There are a lot of subtle issues involved, a lot of choices that we, as theorists, need to make. And at the end of the day we should judge on the basis of empirical performance and economic plausibility. There is room for reasonable people to disagree here.

Now, on to your reply:

"Suppose the central bank sets the money supply. Assume perfectly flexible prices and rational expectations."

OK, so right away, let me quote from Steve's paper in this regard: "Specifying the relationship between fiscal and monetary policy will be critical to how this model works. First, we will write the budget constraints of the central bank and the fiscal authority separately, so as to make clear what assumptions
we are making." Are you sure what you are saying now is consistent with the assumptions Steve is making in his model?

"1. If the central bank increases the growth rate of the money supply, the inflation rate will rise by the same amount, and so will the nominal interest rate. Standard Fisher Equation result. But Steve has identified a minimum equilibrium rate of inflation, call it zlb. And associated with that zlb rate of inflation, there must be a growth rate of the money supply (the same zlb, assuming the economy is stationary). ***What happens if the central bank drops the growth rate of the money supply below that rate zlb?*** Would Steve (or you) say that cannot happen? But it *can* happen. If the printing press breaks down, or if some notes get lost, it *will* happen. What then? Can't inflation drop below Steve's minimum zlb level? It must, and if it does so, then Steve's equation 1(?) will be violated, and markets will not clear. There will be an excess demand for money, and excess supply of goods, and inflation will fall without limit."

You are assuming that the inflation rate is determined by the money growth rate. This is fine in some models, but I don't think this is the case in Steve's model. In his model economy, the inflation rate is determined endogenously in equilibrium. So while the question "what happens if the CB drops the growth rate of the money supply below X" is an interesting question, I don't see what it has to do with the mechanism Steve is trying to explain.

"2. If the central bank increases the money growth rate that will cause an increase in the inflation rate and an increase in the nominal interest rate. But we cannot reverse causality and say that if the central bank increases the nominal interest rate that will cause the inflation rate to rise. Sometimes we cannot reverse causality statements. If I press down on the gas pedal, the speedometer needle will rotate clockwise. But if I grab hold of the speedometer needle, and rotate it clockwise, that does not cause the gas pedal to go down."

I like that analogy. However, direction of causality is often difficult to determine (unlike your example). And so, as economists, I think we should feel free to consider all possibilities. This complaint, btw, reminds me of the problem you had with Kocherlakota's speech. It is well taken and, indeed, I pointed to a paper by Peter Howitt that formalized the view you were expressing.

"3. For 20 years (and more) the Bank of Canada (and others) has followed this procedure: if inflation looks like it's heading below 2%, *lower* the nominal interest rate to increase inflation; if the inflation rate looks like it's heading above 2%, *raise* the nominal interest rate to decrease inflation. Are you saying the Bank of Canada has been turning the steering wheel the wrong way? If so, it must have been a miracle that inflation averaged almost exactly 2% over the last 20 years. Because if a bus driver thinks you need to turn the steering wheel clockwise to make the bus turn left, he would almost certainly start veering off course almost immediately, and just run in circles."

This argument is completely different than your previous two in that it relies on empiricism rather than theory. I agree with the point. On the other hand, inflation in the US is falling as the Fed's balance sheet continues to expand. And on the other hand again, things look a little different in Japan.

This is all very interesting! (Not sure what calling each other stupid is supposed to accomplish.)

[The Keystone Garter]

...the most likely way the printing presses would break down is if there is too much federal debt or if deficits caused by the debt are too high.

[Adam P]

BTW David,

Can you remind me, was SW, like Krugman, calling for a much bigger fiscal stimulus?

Also, why did he sum up the blog post with cheap shots at the Fed instead of strongly advocating for a much higher fiscal deficit?

[stearm]

Well, David is saying that Williamson wrote an article about monetary policy in order to support the idea that expansionary fiscal policy is the only solution to end a shortage of safe assets. I am puzzled.

[Mike Sax]

David:

"But the real solution is a short term increase in Treasury debt -- something beyond the power of the Fed to accomplish. This is a policy recommendation that I'm sure Krugman and DeLong would favor. The fact that they (and you, and Nick, and most others) did not catch it demonstrates that you nobody really bothered reading Steve's papers before joyfully portraying him as an ignoramus"

I for one did notice this.

http://diaryofarepublicanhater.blogspot.com/2013/11/stephen-williamson-on-zlb-interest.html

As I argue, SW's argument is much less anti-Krugman as he agrees with him at bottom regarding the liquidity trap-if anything he sounds more pessimistic than Krugman himself on monetary policy at the ZLB. He's much less anti-Krugman in policy implication than anti-Sumner-anti Market Monetarist in general.

It makes more sense for Nick to bag SW than Krugman and Delong in that sense.especially as SW favors an increase in govt debt: what could be more Keynesian than that?-other than that SW is always razzing Krugman personally.

On the other hand, it seems that the battle lines drawn here are between freshwater-saltwater rather than simply Keynesian-anti Keynesian. As SW has been identified with the freshwater school, that might explain the animus against him from Krugman-Delong.

There's been a lot about the FW-SW divide lately, for example, Miles Kimball and Noah Smith.

http://qz.com/150779/the-shakeup-at-the-minneapolis-fed-is-a-battle-for-the-soul-of-macroeconomics-again/

[Nick Rowe]

David: "(Not sure what calling each other stupid is supposed to accomplish.)"

I am definitely not saying Steve is stupid. To take just one small but immediate example, the post he wrote immediately before this one was a very good post. But there is a massive problem with this post. And it really worries me that he, and presumably many other economists, can't see it.

Gotta go cook dinner.

[Majromax]

Maybe the problem isn't that the Fed is increasing the money supply, but in how it's doing it?

QE relies on asset purchases, meaning that the currency in issue is supported by a real-life security on the Fed's balance sheet. That makes the dollar not just a fiat currency, but "backed" by the mix of assets held by the Fed.

While I can't take a US Dollar to a Federal Reserve bank and redeem it for a tiny fraction of the Fed's balance sheet, I'm not sure that's important by itself; everything held by the Fed has a fixed maturity date that will ultimately result in redemption, possibly with additional rollover with new purchases.

Since the financial crisis and QE, the ratio of money supply (whatever measure you choose) to Fed balance sheet has dropped:

(Note the MZM ratio has a different scale by a factor of 10, to keep the lines more visible)

If we're willing to extend the analogy a bit far, if this were still the day of the gold standard then the Fed would have increased the supply of money by purchasing more gold. It increases the base money, but it's not obvious that the resulting money has to circulate.

(That's also what we've seen in that QE has increased the money supply but the money velocity has also dropped.)

[David Andolfatto]

Adam P:

"Can you remind me, was SW, like Krugman, calling for a much bigger fiscal stimulus?"

I am not sure if Steve did so explicitly, but I certainly made that suggestion (a suggestion based on the same type of model Steve is studying); see: http://andolfatto.blogspot.com/2011/11/not-enough-us-debt.html

"Also, why did he sum up the blog post with cheap shots at the Fed instead of strongly advocating for a much higher fiscal deficit?"

Adam, why don't you ask him that question? I wouldn't have written it up that way. Maybe he would have phrased it differently now, in light of the reaction. Who knows? It's a goddamn blog post; cut the guy some slack.

Mike Sax:

"...other than that SW is always razzing Krugman personally."

I've been following their exchanges from the beginning and believe me, the first low blow was not fired by Steve.

"There's been a lot about the FW-SW divide lately, for example, Miles Kimball and Noah Smith."

I have a high regard for both Miles and Noah, but with all due respect, that column is not their best effort. In my opinion, Mark Thoma nailed that controversy: http://economistsview.typepad.com/economistsview/2013/11/minnesota-fed-president-and-research-department.html

Stearm:

"Well, David is saying that Williamson wrote an article about monetary policy in order to support the idea that expansionary fiscal policy is the only solution to end a shortage of safe assets. I am puzzled."

I did not say that.

[Kevin Donoghue]

David Andolfatto: "I've been following their exchanges from the beginning and believe me, the first low blow was not fired by Steve."

AFAIK the beginning was April 2010, when Stephen Williamson was writing this sort of thing:

On his New York Times Magazine piece, "How Did Economists Get it so Wrong?. "There was no personal invective in what I wrote. I never insulted anybody's personality. It was always at the level of ideas." Sure. In that piece, Krugman essentially argued that all of macroeconomic research since 1970 was a waste of time, and we should go back to IS-LM. A reading of the piece makes it clear that Krugman is essentially ignorant of macro post-1978, so it's remarkably conceited of him to think he can stick his neck out and make such bold statements. The economists I see most often have spent most or all of their careers trying to contribute to advancing macroeconomic thought, and it should not be hard to understand that they might be unhappy, indeed insulted, by Krugman. To have some ignoramus with a Nobel Prize telling the world you are an idiot doesn't go down well.

I'll be surprised if anyone can link to a Krugman attack on Williamson which predates that delightful offering.

[Mike Sax]

David, I'd be interested if you could link me or point me to where this first shot was then. All I know is that SW writes a lot about Krugman-99.9% in a very pejorative way-where Krugman for his part seldom mentions him at all.

Was it something Krugman said publicly?

[Mike Sax]

Right Kevin-SW seems to confuse Krugman getting personal and many who felt criticized by what he wrote taking it personally.

[Nick Rowe]

David: "OK, so right away, let me quote from Steve's paper in this regard: "Specifying the relationship between fiscal and monetary policy will be critical to how this model works. First, we will write the budget constraints of the central bank and the fiscal authority separately, so as to make clear what assumptions we are making." Are you sure what you are saying now is consistent with the assumptions Steve is making in his model?"

OK, so when I read that, I thought to myself: "Maybe, just maybe, Steve is using the Fiscal Theory of the Price Level, (aka some sort of Pigou effect) to pin down the price level. So if the ZLB binds, and there is excess supply of goods, and inflation starts to fall off the bottomless cliff, and we hold the total nominal value of government liabilities constant, so their real value now rises, so demand for goods rises back to market-clearing levels, so the price level stops falling, so the cliff is not in fact bottomless".

But in the second of Steve's papers, he says:

"The …fiscal authority in our model is assumed to have access to lump-sum taxes, and manipulates taxes over time so that the real value of outstanding government debt (the debt held by the private sector and the central bank) is constant forever."

So it seems that is not what is happening in his model. (Plus, it would be a very different model.)

I think it's simpler than that. I think that Steve thinks: "well if the central bank increases the nominal interest rate by 1ppt, this must cause the inflation rate to rise by 1ppt too [remember the Narayana Kocherlakota controvery a few years back when Steve said this too], and therefore if nominal interest rates cannot fall below some zlb level, that means inflation cannot fall below some zlb level too, and anything which pushes down the equilibrium real interest rate must therefore push up the inflation rate too."

If Steve were just some random person on the internet, it wouldn't matter (much) to me if he said things I thought were totally wrong. But he's a lot more than that. (And so are you.) So I get upset, and worried about the future of economics. So you and Steve are just going to have to get this point right. I'm going to do my (inadequate) best to make damned sure you see the problem and get it right.

Suppose I drew a (normal) supply and demand curve for apples. They cross at P*. I then say to my students: "If P were hypothetically less than P*, there would be excess demand for apples, and some buyers wouldn't be able to buy what they want to buy, so an individual firm, noticing these rationed customers, would see an opportunity to profit by raising its individual Pi above P. And all firms would do the same, so P would rise back to P*. And if P were > P*, there would be an excess supply, and some firms wouldn't be able to sell as many apples as they wanted, and an individual firm would cut its individual price below P, and all would do the same, and P would fall back to P*."

But if I drew the supply curve sloping down, and the demand curve sloping up, I wouldn't be able to say that.

What would happen if hypothetically inflation were to fall below the zlb in Steve's model? The real interest rate would now be too high to satisfy the Euler equation at potential output. What happens next? Nearly all economists would say there would be excess supply of output, so inflation would fall further.

[Nick Rowe]

To ALL commenters: the ONLY thing that matters is that David and Steve (and anyone else like them) gets the point about why I (and others like me) have a problem with Steve's post. (Or, if you want to argue my point is wrong, go ahead.)

Who said what about whom first, and politics, and anything else, is off-topic.

[primedprimate]

Nick: "But I'm not sure it is just about stability in this case."
Nick: "But if I drew the supply curve sloping down, and the demand curve sloping up, I wouldn't be able to say that."

I am not sure I understand why this isn't simply a stability issue. Nick, could you may be try one more post (or comment) to explain your reasoning?

Are you saying that if we find ourselves in a contradiction, then any of the antecedents could be false rather than merely the cherry-picked one? In any case, I would greatly appreciate a follow-up.

[David Andolfatto]

Nick,

I get your point (I do not wish to speak for Steve). In fact, it was I who (in that Narayana Kocherlakota debate) pointed out Howitt's paper on the subject. So yes, I understand your point.

Now let me see if you understand my point. The stability properties you are hanging your hat on depend on a particular *theory* of the way the world works (in Howitt's model, it is adaptive inflation expectations). If one adopts a different theory of inflation expectation formation, say, to take an extreme case, of the type assumed by Schmitt-Grohe and Uribe, then the "little arrows" drawn by Krugman are *reversed.* It is the deflationary equilibrium that becomes stable. (See: http://andolfatto.blogspot.com/2013/01/is-it-time-for-fed-to-raise-its-policy_19.html?showComment=1374334899682)

Now maybe you think that theory is crazy. That's fine. But what we're talking about here (in my view) is competing *theories.* You can't just tell someone that they're wrong because they subscribe to one or the other. Probably both contain an element of truth. And in any case, they should be judged by their capacity to interpret the world in a plausible way.

By the way, I'm not entirely sure that the issue with Steve's model is a "stability issue." The result he reports is true even away from the ZLB.

[JP Koning]

"I think it's simpler than that. I think that Steve thinks: "well if the central bank increases the nominal interest rate by 1ppt, this must cause the inflation rate to rise by 1ppt too [remember the Narayana Kocherlakota controvery a few years back when Steve said this too], and therefore if nominal interest rates cannot fall below some zlb level, that means inflation cannot fall below some zlb level too, and anything which pushes down the equilibrium real interest rate must therefore push up the inflation rate too.""

Thanks Nick, I finally figured out what Steve seems to be saying in his post. Correct me if I'm wrong, but he's just taking the Fisher equation nominal interest = real interest + inflation, then if we are stuck at 0 nominal interest and a liquidity premium develops in bonds so that real interest is lower than it otherwise would be, then inflation must by definition be higher. But he's just manipulating a formula... there's no real story about how things play out.

[edited by NR for typo clarity]

[Adam P]

But David, isn't part of the point here that rational expectations is an equilibrium concept? Is there a notion of rational expectations out of equilibrium?

Thus you can't try to make this a competing theories problem because it's SW that lacks a competing theory.

I think I can safely paraphrase Nick as saying that a model that doesn't specify the off equilibrium behaviour that enforces the equilibrium under study is incomplete and thus not useful for making the sorts of strong conclusions that SW wants to make.

[David Andolfatto]

Well thank you everyone, you've motivated me to consume a large part of my weekend with this post:

http://andolfatto.blogspot.com/2013/12/is-qe-lowering-rate-of-inflation.html

Looking forward to your comments. Cheers!

[Nick Rowe]

primed: "I am not sure I understand why this isn't simply a stability issue. Nick, could you may be try one more post (or comment) to explain your reasoning?"

I'm not sure either. Let me try this:

Suppose we drew a standard vertical AS curve, only with inflation on the vertical axis. Now suppose we also drew a vertical AD curve, exactly on top of the AS curve. Except the AD curve stops dead at at inflation rate zlb, and disappears below that.

JP: Yes, I think that's right.

Adam: yep. I want at least some sort of informal story that makes sense of the off-equilibrium counterfactual conditional.

David: I will go read your post. I went out for a snowy walk, and was thinking about whether I could make sense of what Steve is saying by adding some sort of Pigou effect (what we used to call it in the olden days)/FTPL (what young people call it nowadays).

[Andy]

I'm new to this, so entirely possible that I'm missing a bunch of assumptions behind the scenes, but.. seems to me that where SW has gone wrong is he is confusing *expectations* of something with what actually happens. In his equations, folks are making decisions that maximize their utility based on expectations of the future. When liquidity preference rises, in order to induce someone to make that next purchase or investment, the current price has to fall enough that it seems like a good deal, given an increased desire to hold cash (or whatever). You can call that expected inflation if you like (implicit in this is that these actors expect prices to return to "normal") , but it's a little misleading. But the net effect of that on current prices (and in the near future as it plays out) is deflationary pressure.

I guess I think his mistake is a bit more fundamental than "right equations, wrong interpretation".

[Andy]

BTW, I think this problem is a close cousin to the one you described earlier about the OK/NK paradox of anchoring - you can describe the situation as current relatively rapid deflation deflation followed by expected inflation, or just expected inflation; the equations don't necessarily tell you which is right.

[perfectlyGoodInk]

"This is not about politics or ideology. Explaining everything in terms of politics or ideology is one of those witchcraft explanations that only ignorant people use, who practice witchcraft themselves, and so think everyone else is a witch. I am pretty sure I am more right-wing than Steve is. This is about how we do economics."

Not everything wrong with macro derives from politics or ideology. Personally, I also think the field needs less math and more computer simulations (and I think even economists have a tendency to honor sunk costs like their mathematical training and expertise). I just think that one of the bad incentives upon macroeconomic research is that one of the variables affecting the usefulness of a macroeconomic model is whether it furthers a particular political ideology. That not everybody responds to incentives the same way is true, but irrelevant.

But note that one of the values of complicated math is that it can be helpful to obscure when a model serves an ideological purpose. Also, when value can be gained from being politically useful, the need to accurately model the economy becomes less important, and so losing sight of what the equations represent has less of a cost.

[TallDave]

I'm not sure how useful these models are. The real game is expectations -- as Fisher predicted long ago and Friedman recapped somewhat later, decades of successful low inflation targeting policy have created long-term expectations of low inflation, leading to ever-falling nominal rates, until they've bumped into ZLB. QE doesn't change long-term expectations much, so it doesn't do much to the trend (remember, the Fed target is a continual promise QE won't be inflationary!). At the same time, relatively small surprises have large effects, because money is still too tight since TGR began (so markets care about money, which correlation began in 2008) and surprises DO change expectations.

Imagine Yellen comes in drunk on her first day and says something like "Welcome back to the 1970s folks, we're targeting unemployment and don't care much about inflation!" Or something more sane, like NDGPLT. I think the Fed target matters a lot more than anything else (the Chuck Norris effect), and empirical support for that notion will continue to grow...

[Patrick]

If he wants to use models with equations that are that complex Williamson should learn Latex. Good communication is important, even to the mathematically inclined.