"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.
Worthwhile Canadian Initiative 
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:
I’ll be surprised if anyone can link to a Krugman attack on Williamson which predates that delightful offering.
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?
Right Kevin-SW seems to confuse Krugman getting personal and many who felt criticized by what he wrote taking it personally.
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.
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.
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.
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.
“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]
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.
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!
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).
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”.
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.
“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.
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…
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.