A Major Shock Makes Prices More Flexible And May Result In A Burst Of Inflation Or Deflation

>> John Taylor: So happy to have our colleague Bob Hall speak. I just wrote a few things down. He's been at Hoover since 1978, sorry to say that.

>> John Taylor: Before that he taught at MIT, Berkeley, and believe it or not, he was born here in Palo Alto. I don't know, too many can say that.

That's terrific. President of the American Economic Association, author flat tax. And of course, this 1985 book on macroeconomics with this guy named Taylor.

>> John Taylor: But today, a very good title, maybe this is the longest title I've heard. A Major Shock Makes Prices More Flexible and May Result in a Burst of Inflation or Deflation.

Thank you, Bob.

>> Bob Hall: Thanks, nice to be here. Gonna try to do the standing. Am I getting any amplification or do I need it?

>> John Taylor: You could sit down.

>> Bob Hall: Well, I like to stand.

>> John Taylor: Okay.

>> Bob Hall: Okay, anyway, let's see what happens.

>> Elena: It's hard to hear.

 

>> Bob Hall: We'll see. Okay, so, self-explanatory title. This works its way through three propositions, and there'll be a proposition slide for each of the three. Just so you see, this is the only introduction you're gonna get.

>> Bob Hall: Large increases in price flexibility in the presence of menu cost, price stickiness.

So this is going to be an exercise in a topic that I stayed away from in 55 years of my career until this year. But I never said it was wrong, I just said I wasn't interested in it. And then suddenly I got interested. Then, moving on, the volatility of cost shocks, rises in crises such as the financial crisis and the pandemic, and then finally episodes of runaway inflation or deflation, may not necessarily, this is gonna be very important point.

There may be bursts of inflation or deflation when large fraction of prices become flexible because they're outside zone of inaction. And so it's a pretty obvious proposition. And of course, I'm just waiting, Ken and I were chatting about this before. There may be part of the analysis in the first section that has been done before and some part of the huge literature on SS models, which this is a contribution to.

But I haven't seen it, at least in the Calvo-type literature, where the object of interest is a price that's set. But stand by on that. I could easily imagine sometime in the next six weeks that I'll get an email with a site says, this has all been done before.

 

>> John Cochrane: Only cost shocks, I mean, intuitively, we would think that a big demand shock would lead to more flexible prices, too, as happens in our-

>> Bob Hall: Stand by.

>> John Cochrane: Okay.

>> Bob Hall: Answer, no, but there are other sources of shocks, in fact, I'll document other shocks. So you're half right and half wrong, as you'll see.

Okay, so this is a contribution to the branch of the sticky price literature that's associated with a very well-known paper by Golosov and Lucas. And a lot of what I do is tied to the same setup, it's in their paper, simplification of it, but the same basic idea.

But the goal, the aspect of the behavior that is identified in that paper is quite different in the take that I have compared to what Golosov and Lucas do. So the key thing is that this belongs to the broad class of SS models where there is a cost of action, which generates, in terms of behavior, the zone of inaction, where the agents are, because it occurs at a setup cost, a menu cost, as it's called in this literature.

And that's central when they engage in what's called a reset. It means that they have cleared that, it is now worthwhile to take an action rather than just sticking where you were before. So there's a contrast here between two actions, one is stick and the other is reset.

And then the question is, what interesting things can we say? And focusing entirely on this question of whether you can get a big enough change in the regions relevant in that literature to get big differences in crises than in normal times. So this is a crisis is something like most recently, of course, it's the pandemic.

And before that, you'll see both the pandemic and the financial crisis have big, big, big changes in the determinants of the zone of inaction, with a much higher probability of the price winding up out of the zone of inaction, that is, getting a reset. And a reset then eliminates price stickiness.

So this is a theory that in crises the Keynesian economics becomes irrelevant in crises because there's no price stickiness left, that's the one simple way of explaining the idea. I've only located one paper, but there is one paper by Joe Bavra about ten years ago that sort of mentions this on the fly, but it's become, in my development here, it's this kind of the centerpiece.

 

>> Speaker 6: The slide said it's a fixed markup over cost, cost at the time you reset, or expected cost, or what? What's the cost concept?

>> Bob Hall: Okay, it's optimal in this class of models to make an adjustment, that is, effect, whose amount can be deduced without having to To look into the future in spite of that, it's because you know that you'll make the same decision in the future as currently.

So, the technology here is Dixit Spence Stiglitz and so you get a markup on cost changes. Price needs to change when cost changes. And getting back to what John mentioned, that technology or that market setup is one in which there's no response to a change in demand. The cost is the pure determinant cost and productivity and market power.

Three, there are three sources of volatility, but demand is not one of them. So price is not affected by demand. That's a fundamental principle that Dixit Stiglitz.

>> Speaker 7: Because they don't have a fixed input like capital in their model.

>> Bob Hall: Agreed.

>> Speaker 7: Yeah.

>> Bob Hall: This is really stripped down.

 

>> Speaker 7: Yeah.

>> Bob Hall: Sure. But I think you can see your way to complicate it in the world by putting in capital. And then, of course.

>> John Cochrane: If you know costs are going up in the future, you don't raise prices more now because they're going to be stuck there for a while.

 

>> Bob Hall: No, not in this setup. Well, no, I'm sorry. You know what the future is going to look like, and you know that you may, the price you're setting now may apply in the future, but in the future, you would want to choose the same prices today. So you can infer the price without having to do what looks superficially.

And some branches of this literature, like which maps in all these expectations. This is doing new keynesian models in which expectations have no real important role, which is something that I've always craved. I always thought that it's fundamentally confusing in the way that new keynesian literature is usually written up, that all that matters is expectations of the future.

That's not, it turns out not to be true in this setup. It took me a while to figure that out. Okay, so I've discussed most of the features of this model. There's simple technology. One unit of input makes one unit of output, I'll mention a little bit later, changes in productivity, which then introduce another source of volatility.

So this is stage one. And those are stage two, where market power, which I ignore at this stage, comes into the story, too. Okay, so the firm, so we're going to describe the world as seen by one firm, but the economy has many firms and certainly in any reasonable application of this, those firms are heterogeneous.

Some are chronically in their sticky price range and some are chronically flexible price and then others, which are the interesting ones will go from one to the other depending on the volatility of cost. So that's where this is headed. Okay, so there's a random variable in each firm, which is its input cost in this first exercise, which is a random variable and I'll tell you its distribution shortly.

The price elasticity of demand is two. Now, why is it two? I don't know. Has anyone else ever found this two is just a uniquely convenient. It makes everything about the SS model just completely transparent and follows almost no math, almost all the math. All you have to know is the quadratic equation, which I think most of us can remember.

We can always look it up on wikipedia. But that's the only math you need to know to follow this because of having price elasticity of demand of two. Okay, so that means that the demand function is one over p squared. It means that the markup ratio is two, so that when the reset occurs, the reset will be to two times cost.

So that you get this, in this rather extreme market power, you double, you sell the product for twice its marginal cost.

>> Speaker 8: Is this a one period model or are you anticipating prices might change again?

>> Bob Hall: Well, it's cost you need to restate that. Well, if cost changes again, you're gonna get a, you're not gonna use this price.

 

>> Speaker 8: But I'm wondering, in a multi period model whether you go all the way to the current optimum or what

>> Bob Hall: you do.

>> Speaker 8: You would?

>> Bob Hall: Yes.

>> Speaker 9: When free of menu cost. Yes, zero menu cost, okay.

>> Bob Hall: Well, okay, anyway, there's no, the only optimization that the firm does is called upon to do is the one to figure out the markup 100% double cost.

This is all me trying to really simplify this problem. I think it makes it quite obvious what's going on. So, in practice, obviously, there's all kinds of reasons that the future might matter would come in, but this particular specification gets rid of it. Okay, so then there's a cost kappa to make a price change.

And therefore, the profit function is two c minus c. That's price minus cost divided by the quantity, which is two c squared. So that's the gross profit but then you have to net out the cost of making that change, which is Kappa. And then the question for the firm is, how does that compare to.

So, first of all, that simplifies to one over four c minus capital.

>> John Cochrane: Bob, here, you just assumed that the price is gonna be two c as opposed to deriving the price is gonna be two c.

>> Bob Hall: Yeah. I told you the demand function. So there's optimizing against the constant elastic demand function standard.

 

>> John Cochrane: But now I have an intergeneral problem that I can either use the old. Price recognize the new price and if I set the new price, then that's a constraint on tomorrow's cheap price races. So how do you know?

>> Bob Hall: But the problem you might be solving next period has the same solution.

 

>> John Cochrane: So what is the state variable of what was yesterday's price in it?

>> Bob Hall: Okay, yeah, you'll see how this evolves, you're in firm territory now.

>> Elena: Can I ask, I think I have a similar doubt, so what's the process for c?

>> Bob Hall: I'll tell you that slide coming up.

 

>> Darryl: That was my question.

>> Speaker 11: If Daryl's confused, and I don't think

>> Darryl: I'm not confused

>> Darryl: You're not addressing that dynamic of partial adjustment.

>> Bob Hall: Okay, so I spent a lot of time thinking that I needed to introduce an assumption of, there were intertemporal issues that came should come in, but because there was 100% discounting.

But then it turned out that wasn't right. Anyway, if I'm wrong on this, someone's gonna have to straighten it out.

>> Speaker 7: Well, price is a state variable when there's menu costs, right? I mean, that's kind of the point we're making.

>> Bob Hall: Yes, absolutely.

>> Speaker 7: It is a state variable.

 

>> Bob Hall: Yeah, yeah, yeah, I'll show you. Yeah, yeah. Yea, there's the law of motion. It's coming up.

>> Speaker 12: So your firms don't intertemporally optimize, you just said something about 100% discounting.

>> Bob Hall: No, no, that's what I thought, then I realized that when they're optimize, they do exactly the same thing that they would have done.

This is, of course, leaning very hard on this special feature of dixit cigarettes.

>> Speaker 12: So that's an exercise for the interested reader to go prove for ourselves that you don't think about the fact that when you set a price today, you're changing a state variable for tomorrow's price changing decision.

 

>> Bob Hall: Yeah, it doesn't show up in the. Okay, well, I spent a lot of time working on this and I finally talked myself into this position. But for a long time, I was just saying I'm assuming that the firm has 100% discount rate.

>> Speaker 12: I'm with you.

>> Bob Hall: Okay, fine so that would be fine if it recurs.

 

>> Speaker 12: Okay,

>> Bob Hall: This is just trying to make it clear. When I started this project, I thought, well, it's sort of obvious that if there's more dispersion of cost that there's gonna be more firms outside there. And I don't need to say more than that, but then I get pressure from audiences that we want more of a story.

 

>> John Cochrane: I'm not being critical I would like to learn how to use this model and that seems like the first thing the referees are gonna ask me is. Why do we go, right,

>> Bob Hall: This paper will not be published, and this issue is completely resolved.

>> Elena: Also, the cost process, I was thinking maybe have some persistence to it.

 

>> Bob Hall: Okay.

>> Elena: In which case,

>> Bob Hall: I thought about that, too. Okay, there's no persistence. Yeah. What I'm gonna talk about is explicit. If there's persistence, you get a, of course you get the corresponding law of motion, but we're not gonna get into that territory. Resistance is assumed away, and I don't think that that is really much of a problem.

Okay, so then on the other hand, if you don't re optimize, you're exploring what would happen if you stuck with what you inherited, then that's just the project. So today's cost and the price that you've elected to retain,

>> Bob Hall: that generates a profit of p tilde minus c or p tilde squared.

And then we're looking to designate the zone of inaction. So the boundary of the zone of inaction is the point where the two parts are identical. That's this equation, here's the magic. That's a quadratic equation if the

>> Bob Hall: demand function has elasticity of two. Otherwise, that's key because you want the upper end and the lower end, sorry, the lower end and the upper end of the zone of inaction suggest that there should be two roots.

You get that automatically from the quadratic otherwise, you have to do some more math. So wanting to keep this really streamlined, I am satisfied that though the conclusions that get to, which are quite surprising apply, they're not unique to elasticity of. They would retain the simplicity of the constant elasticity demand, which a lot of us lean on very hard.

All right so I said that. All right, so I hope you can see this.

>> Bob Hall: Anyway, it's customary in this literature to assume that cap is a pretty small number, cuz if you're making a big deal out of a huge number, then that's just something. It just can't be, that's that expensive to change the price.

So it should take a small number that's representative of this literature. And then you get, there's the zone of inaction and of course, it's by the lagged price, as somebody mentioned. And there's two roots, and they correspond to the block boundaries of that zone. So that means that if you look at the choice problem then price is a function of cost then you get this configuration.

 

>> Speaker 13: Do these two graphs come from your equations? Can you get these two graphs from the equation?

>> Bob Hall: Sure, yeah, straight away.

>> Speaker 13: So maybe show me, show us.

>> Bob Hall: Well I showed you a quadratic equation, I guess I assumed that. You remember minus b plus or minus squared minus four ac all over two a.

 

>> Speaker 13: Here's a kink in the middle, where does the kink come from?

>> Bob Hall: I think is because you're not changing, you're taking advantage of

>> Speaker 14: zone of inaction. Is this interval Pinned down by the two solutions to the quadratic.

>> Bob Hall: Yeah,

>> Speaker 14: so that's why the price decision doesn't depend on the cost and then outside that is then when the markup.

 

>> Bob Hall: Yes, that's right the vertical axis was price on that diagram. So the whole rest of the paper is this. Just going to look at how this model works. Now we come up to the question of cost chalk. And the cost is drawn from a uniform distribution on an interval, whose boundary is a parameter.

So, when that parameter delta is small, it means that there's a very broad support. And if Delta is close to one, then it's very narrow. So it's a measure of the dispersion.

>> Bob Hall: And the mean of the cost shock is always zero. Sorry, it's always one. So Delta, there's exactly the same amount of probability above as below.

So, obviously mean is one. So it's a mean preserving spread. Okay, then, that's the quadratic. Now restated in terms of the state variable PT minus 1. So you can see exactly how the lag price. So, if you're on the left side, that's the reset side, then you reset the price.

And if you're on the right side of that, it's better not to. All right, so you can write this down as a time series process. And this is the part where I'm in way over my head, but you can see that this is a highly nonlinear, first order difference equation.

And there is an important question of whether or not the result of that is ergodic. In other words, is it sort of self replicating? In particular, the definition is the mean of the process, the same over different intervals that you've taken it. So, for example, a non ergodic process, a random walk is non-ergodic because it has a random variable concealed within it where the random walk started that varies over time.

So, from what I've dipped into in the math of this, there's not a lot of math that tells you. That answers this question directly if you give it, say, a first year, a first period, first order difference equation in this form. So, I turned to just doing this mathematically.

And it's extremely cheap to do a lot of math with this difference equation because it has, especially because in the elasticity of the demand, elasticity of two, it's a trivial piece of math. So you can do a huge amount of, monte Carlo, John?

>> John Cochrane: Yeah, I'm still kinda a little stuck on the dynamics.

So I understand that these cost shocks are IID, start at one and it's up, it's down, it's up, it's down. Now, I get a cost shock out at 1.3. And I'm thinking do I wanna raise my price to 1.3? The fact that I know that next day's cost shock is not gonna be centered at 1.3.

It's gonna be centered around one again. Would seem to make a big difference on why don't I just leave the price alone at one. Cuz tomorrow I'm gonna be IID around one again, IID not around 1.3. If I raise my price to 1.3, I'm pretty darn sure that I'm gonna have to change it again tomorrow.

 

>> Speaker 15: I think you got to stick with 100% discounting.

>> Speaker 16: Yeah, that's right.

>> Bob Hall: You know what, I. Okay, all right, anyway.

>> Speaker 15: Yeah, because you agree, if it's 100% discounting, then.

>> Elena: It doesn't matter.

>> Speaker 15: This is all fine.

>> Bob Hall: Yeah, okay, well, Stan, okay, that's fine cuz I was perfectly satisfied with that until I convinced myself that I didn't need to make that assumption.

 

>> John Cochrane: Are the cost sharks gonna be random walks, or are they gonna be IID?

>> Bob Hall: They're IID.

>> John Cochrane: Okay, so, if I see a big cost shock, I kinda know that tomorrow I'm drawing from, not this cost, I'm drawing from that cost over there. So,

>> Speaker 15: I don't care about tomorrow

>> John Cochrane: Unless 100% discounting, I'm gonna want to just leave the price alone cuz I know we're going right back tomorrow.

 

>> Bob Hall: No, the counterargument is that, the decision you make in that setting, in terms of setting a price, is the same. It follows the same decision rule,

>> Speaker 15: but the state is different. Okay, this is a recursive optimal control problem, recursive dynamic programming problem.

>> Bob Hall: Yes, I agree with that.

 

>> Speaker 15: If you have sufficient mixing, then it's gonna be ergodic. You don't have any explosion stuff going on here like a random walk. But because everything's bounded.

>> Bob Hall: So you know a theorems that would apply.

>> Speaker 15: Basically it's if you have a Markov process such that every, there's a positive probability of state I visiting state j, then you have a narcotic distribution.

It's only if you have Islands of states that just once you're there you stay there. But then you don't have,

>> Bob Hall: Okay, well you, but you do have that, so.

>> Speaker 15: No, you.

>> Bob Hall: Picture.

>> Speaker 15: Yeah, if your delta is big enough relative to the kappa, then it's gonna get mixed around, because with a delta big enough.

No matter where you are, you're gonna get hit that you wanna change it.

>> Bob Hall: Well, somewhere, there's a picture. Yeah, I guess it's after.

>> Speaker 15: Whereas if delta is zero, basically there is no shock, and basically you just stay wherever you started. Now that process is not ergodic.

 

>> Bob Hall: Okay, well we could, but.

>> Speaker 15: So, if you make delta big enough that kicks things around enough, then it's gonna behave nicely.

>> Bob Hall: Okay, so here, this is how this process evolves.

>> Speaker 15: Yeah.

>> Bob Hall: This is an experiment with a huge number of observations. It's 300, anyway, it's a lot.

I forget anyway, it's an infinite amount of arithmetic. Just barely see that there's a, just, there's a little bit of effect, I'd have instead of having a million, if I did it 100 million times, which I could easily do, it would be even smoother. But I think you can see the point that, and this is, so, this is the relation between the shock size, which is controlled on the horizontal axis by the parameter delta.

And then, for each of the million observation vectors that it's generated. What fraction of them, of those observations involved a reset. So this is the reset fraction. So on the left, there isn't enough stirring up, just what Ken was talking about. It's not being stirred up enough so that you just always stick.

And that's the end of the story. And this is what's crucial is that then at a particular level, which is a little below, you can see it's a little below 0.09. Then you get this seemingly discontinuous, but it's actually not discontinuous, it doesn't really matter, but the conclusion would be the same, but I explored that pretty carefully.

But there's a key value just under 0.09 where you're suddenly getting a substantial volume of resets. And if you go up say to a delta of 0.25, then you get 70% of the time you're resetting the price. The relationship is that, you snap upward to about 30% resets very soon after you cross this key point, which is about 0.09.

So it's wonderfully nonlinear, and that's exactly what we're looking for here. So firms that start out in normal times, just to the left of that, let's see.

>> Speaker 17: So what are you simulating to get this, thousands of simulated, what do you-.

>> Bob Hall: Just running, it's a first order difference equation, highly nonlinear-

 

>> Speaker 17: Of the ones that you showed us?

>> Bob Hall: So you're generating a time series just by iterating this here, it's a first order difference equation, and you're generating-

>> Speaker 17: You had them for previous slides? Pt is equal to f{pt} minus 1 and then current.

>> Bob Hall: Yeah, it's current cost.

So that difference equation, pt depending on pt minus 1?

>> Speaker 17: And then cost is an IAB shock.

>> Bob Hall: Yes.

>> Elena: Minus forward.

>> Bob Hall: Yeah, is that clear now?

>> Speaker 17: Well, what causes the sharp movement up, what causes that?

>> Bob Hall: Go back a slight to that discontinuous function.

>> John Cochrane: Yeah, it's not a normal distribution to shock.

The shock can never get you out of the discontinuities,

>> John Cochrane: Just what you get.

>> Bob Hall: I had no idea this is the way it would come out. It's not rigged at all, it just happened to be. You can see first of all that, you can see that if the shocks are small enough, you never get kicked and since they're IID.

 

>> Speaker 17: Yeah.

>> Bob Hall: You get the support of the shocks is contained within that area of not responding, so you just don't respond. But then if you start responding, then of course that means you are sensitive to what the shock does and the shock will then start kicking you up much.

But furthermore, that's why that almost discontinuity.

>> John Cochrane: But that's because you started with a lag price of one. You had started with a lag price of 1.05. And even small shocks would get you out. And then once you're out, you wanna come back.

>> Speaker 17: What is the lag of 1.05?

 

>> Bob Hall: You'll go in, if you're outside the zone, you'll immediately go to the middle of the zone, and for the rest of the time, you'll just be in the middle of the zone. So these things are stated correctly, except for the very first observation, which could be start outside.

But if it does start outside-

>> John Cochrane: But then you go right back.

>> Bob Hall: You'll go inside for the rest of time. So this is really an exciting finding, because it's exactly claim that I made, but way more powerful result than I ever dreamed of cuz I thought that, well, it'll just be kinda proportional to the volatility of the shock, but instead you get this.

So now we have a theory, and the data, then that I compiled which is-

>> John Cochrane: That comes from the shock distribution. Get a normal shock distribution, then you would at least have a smooth, it would be nonlinear, but it would be smooth.

>> Bob Hall: Well, no, this is smooth, this is a continuous.

 

>> John Cochrane: Okay, but a normal shock distribution would start right away at rising. There would be no period of permanent.

>> Speaker 17: Your shock is smooth, but on a compact domain.

>> Bob Hall: Correct.

>> Speaker 17: Normal has an infinite port.

>> Bob Hall: Correct.

>> Speaker 17: And so then yeah, you're gonna get a lot more kicking around.

 

>> Bob Hall: Sure,

>> Speaker 17: I think it's the key thing here is the support of the shock,

>> Bob Hall: right? Yes, okay, good point.

>> Bob Hall: You think that's gonna knock that this is just a special finding that's-

>> John Cochrane: So it would be gloriously nonlinear,

>> Bob Hall: yeah,

>> John Cochrane: you would start not sitting at zero, and then, boom, but you would start gently going up, and then,

 

>> Bob Hall: it'll, a little. Yeah, sure, okay. Try normal shock, just put your computer one line of your code and we can see what happens with the normal shock.

>> John Cochrane: Yeah, okay.

>> Speaker 17: And then change the variance, variance should be very small, in which case it'll be a lot like your zero case, but then that's going to grow, I don't know, yeah.

 

>> Bob Hall: Okay.

>> Speaker 17: Please, I think the support of the shock relative to this inaction region.

>> Bob Hall: Yeah, yes, okay, that's actually commented in the paper, not drawing that conclusion.

>> Speaker 17: And the uniform has is a very sharp kind of distribution with a very definite sharp relationship to the interval.

 

>> Elena: And tightly parameterized.

>> Speaker 17: And the region of inaction, so you're gonna get your results sound very intuitive given those that combination.

>> Bob Hall: Okay, all right so I guess that that'll be high in the agenda.

>> Speaker 17: Yeah.

>> Bob Hall: Further exploration.

>> Speaker 17: Yeah.

>> Bob Hall: Yeah, cuz this point it's where the support of the shock lies entirely within the zone of inaction that you get this on just discontinuous practically.

It's actually not discontinuous but it sure looks like it is. Okay, well that's helpful. So this calculation was based on 300 values of delta. Ken was talking about modeling it as a discrete Markov process, I think 300.

>> Speaker 17: There's an analogous ones too, right?

>> Bob Hall: So in other words, I took 300 million data.

It takes about 5 seconds on My laptop can't do all these calculations. It's incredible. But that reflects what a simple method is. Okay, so that's the analytical finding, is this. Okay, so now the question is, well, how much? All right, so we've talked about the key finding. Okay, so robustness will now focus on removing the sharp edge of the uniform distribution and giving it a curved shoulder.

And that'll smooth out some of this, but ideally preserve most of it. So an explosion can occur if most firms, most of the time, are to the left. But then every once in a while, there's a shock that takes them over to the right. Then that's gonna generate an economy which has sticky prices most of the time.

But when things get really rough, firms are free to choose a better price and will do so, presumably.

>> Speaker 18: Why do you say, when things get rough?

>> Bob Hall: Higher volatility of cost, higher value of whatever measure.

>> Speaker 18: I was at a Fed macro conference last Friday, and one thing they talked about was the monetary injection that we had.

And so when you have an enormous monetary injection, that's just a one time monetary injection, then, yeah, we know price levels go up.

>> Bob Hall: No, that's not right. Now, that's way, way off base. That completely neglects the fact that the Fed pays interest on reserves. So that shock disappears in the modern.

That's absolutely wrong.

>> Speaker 18: Okay, I'm thinking back, of course, when I was in graduate school, before they started paying interest.

>> Bob Hall: Yes. Okay, well,

>> John Cochrane: it's a completely different world today.

>> Speaker 19: Tim is right cuz it was a fiscal injection. It was not an open market purchase. It was a gift.

 

>> Bob Hall: No

>> Speaker 19: It's just to pay one kind of. Well, anyway, I think this is monetary injection.

>> Speaker 18: Governor Waller talked about this being a monetary injection.

>> Bob Hall: Yeah. Okay, well, that displays remarkable.

>> Bob Hall: How few economists are thinking seriously about the fact that we pay market interest on reserves, but that's what we do.

 

>> Speaker 18: Market interest?

>> Bob Hall: Market interest, yes.

>> John Cochrane: Sometimes more.

>> Bob Hall: Yes, that's right. Yes market interest. Yeah, it's a completely different world, and it's just I'm staggered. Okay. I'm not sure that there's anyone on the board of governors in particular who can really recite how modern monetary economics works.

 

>> Speaker 20: Michael Woodford.

>> Bob Hall: Yes.

>> Speaker 20: Does know. He has learned this.

>> Bob Hall: Exactly, right. You got to read Woodford. Okay. Anyway, how are we doing?

>> John Taylor: You got half power?

>> Bob Hall: That's fine. Okay.

>> Elena: One question, Bob. Can I ask about on the nerdy side? But given that you have a one parameter family, it's not a pure volatility compared to statics you're doing, because you're changing both moments.

 

>> Bob Hall: Changing what?

>> Elena: Both with the first and the second moments of the cost distribution.

>> Bob Hall: No, the cost distribution has first moment, one, non stochastic.

>> Elena: But it's Delta. That's right.

>> Bob Hall: Yeah.

>> Elena: Because it's one plus it's centered around one.

>> Bob Hall: Yeah.

>> Elena: Okay, sorry.

>> John Cochrane: I presume at some point we're gonna do like a network where your price is my cost, the whole system gets more volatile.

 

>> Bob Hall: Well, okay, if this catches on, somebody might do that.

>> John Cochrane: Okay.

>> Bob Hall: I doubt that it would be me.

>> John Cochrane: Well, it should be, right?

>> Bob Hall: It should be, of course. Sure but cuz there's a question of

>> John Cochrane: if I buy from you, then as long as you don't change your price, I don't have a cost shock.

And so we can double the volatility here as soon as you start changing prices. And they become my cost chocks.

>> Bob Hall: Yeah, there's been some work, recent modeling of that phenomenon, but I don't think it is.

>> Speaker 21: Now In the mid nineties, John and I had a student, Alejandro Castaneda, I think is his name, where he solved out this game for a duopoly.

Two firms set their prices, but there's a cost of adjusting the price. I have no idea what the results were. I remember liking it at the time. I don't have a read a copy of his thesis in my library, but no, that was all solved out as a duopoly problem.

That's not a network because it's horizontal release.

>> Bob Hall: Yeah, well, that would be an alternative environment.

>> Speaker 21: Yeah, and the new Keynesian models are horizontal, imperfect competition.

>> Speaker 22: Let's go to the second proposition.

>> Bob Hall: Okay, thank you. All right, so now the question is, is there much volatility to cost shocks?

And the short answer is there's an incredible amount of volatility. So let me go through that. So it doesn't. A lot of modifications that reduce some of the amplification that we just talked about will still bite into just a huge amount of measured volatility. Okay, so this is the measurement approach that I've taken so far, is at the semi detailed 71 industries for which we have quarterly data on input costs.

And on input costs, that's what it's also, in addition, have data on total factor productivity. And so I'll talk about both those. And they look quite similar.

>> Bob Hall: Okay, so let's see, we can expand the universe a little bit. P was equal to two times c, mu times c divided by.

Okay, sorry. Anyway, the parameters mu and a were taken to be 1 in the model but it's clear that fluctuations in and mu and a would have similar effects, because the pricing in the constant elasticity specification has just this simple multiplicative form. But even though I've done a lot of work on mu, I don't trust it and other people don't, certainly not at the fluctuation level.

It's hard enough to get the level of mu, which is an interesting statistic, but it's very hard to find its volatility. So I'm gonna put that aside. But we're gonna look at volatility of cost c and productivity, total factor productivity a in an extended version of the model we just talked about.

Yeah. Okay. So notice that we don't, there's not, there's not a variable called demand. I mean, this is a model takes the model seriously, so it doesn't have demand. There's no object called demand in it. The three things that can affect price are the three, mu, C, and A.

And interestingly, I have done actually quite a bit of work in the same body of data, which also enables me to look at volatility of price. And it's quite low, much lower than any of the three things that make it up. So

>> John Cochrane: if you think of demand as a shift in the demand curve, I see it, But if you think if demand is a change in the elasticity of the demand curve, then-

 

>> Bob Hall: Sure, absolutely, yes, the elasticity of the elasticity, second order-

>> Speaker 23: Ken's point, and this assumes that you can instantly expand supply as much as you want, no fix factors.

>> Bob Hall: Yeah, we're pretty familiar with this kind of environment. Everything is fixable. I think that the two pieces that we're talking about here are gonna survive a more determined attack.

Okay, so there's a BEA data from relatively new source that goes back to 2005, but for this purpose, that includes the two big events that we're interested in, so that's satisfactory. And the statistic here is the cross-sectional standard deviation of the growth ratio. So that's a measure of the volatility.

 

>> John Cochrane: So these are relative prices. Demand has to matter at some point. If we all decide we're gonna measure prices in cents not in dollars, and you would say, well, that's the cost, the nominal cost goes up. But if everybody's nominal cost is somebody else's nominal price, then we'd just bootstrap the whole thing somehow.

 

>> Bob Hall: Yeah, I sat down and thought that all the way through. Now, I'll get back to you on that.

>> John Cochrane: Nominal or input prices here, so the nominal growth rate of input prices.

>> Bob Hall: Yeah, if you change that, it just changes a constant, so it wouldn't matter to the-

 

>> John Cochrane: What is the nominal price-

>> Speaker 24: How things are deflated.

>> John Cochrane: This is a paper about inflation, and you wanna think about the nominal prices being sticky.

>> Speaker 24: That's my thinking as well.

>> John Cochrane: Inflation does have something to do with demand somewhere, and we all kinda get out of whack.

 

>> Speaker 25: Yeah, which also raises another issue about why it makes sense to think of an unchanging interval over which these cost shocks are rising, things are nominal here. The price level is rising, so that interval seems hard. You assume there's no trend in that, but that seems to set aside the issue here.

 

>> Bob Hall: Okay, well, first of all, this issue doesn't arise with TFP, which does have-

>> Speaker 25: It's more plausible that TFP is trendless.

>> Bob Hall: Yeah, that's right, I'll get the same results for TFP, so I can at least fall back-

>> Speaker 25: Even there, at the industry level, that seems unlikely, and the firm level seems even more unlikely that there be trendless TFP.

 

>> Bob Hall: Okay, I came up with a really good answer to this question when I asked myself a few weeks ago, I'll get back to you. I thought about that.

>> Speaker 25: I know you ultimately went to the computer on this, is it that hard to just take a dispense with the 100% discounting assumption, allow for some trends or some more plausible forcing process.

And instead of having your computer do it in 5 seconds, maybe it does it in 5 hours, but generate the same picture you're interested in.

>> Bob Hall: Is that allowed?

>> Speaker 25: Then just sets aside a lot of these concerns that keep coming up, that seems like a feasible approach.

 

>> Bob Hall: Okay, sorry, yeah, it is.

>> Speaker 25: I'm sure King can tell you the most efficient way to solve all these things.

>> Bob Hall: Yeah.

>> Speaker 25: It seems like you're overly tying your hands, so you can solve this in 5 seconds instead of 5 hours.

>> Speaker 25: But no, that's the impression I'm getting.

 

>> Speaker 26: Bob has made a cute, nice little point, which can't be pushed too far.

>> Speaker 25: Okay, but we wanna know how far it can be pushed.

>> Speaker 26: Yeah, and then that requires more computing. Now I see the BEA input, and thinking of John's comment, what about the network?

Some firms are selling their output to be other people's intermediate goods, there's like an input-output matrix. I don't know if that's in the BEA data.

>> Speaker 27: Why don't you show us the quarterly numbers? Yeah, that would be nice to incorporate.

>> Speaker 26: Yeah.

>> Bob Hall: So it's pretty remarkable. Notice that the financial crisis actually generates even more room than the pandemic.

There's also two places, one in 2005 and the other in about 2015, where there was meaningful changes without being associated with any particular. But the two big spikes were two very identifiable crises, yeah. And it's something like a factor of five, I mean, it's huge.

>> John Cochrane: Bob, my cost is somebody else's price, so productivity, I understand, is an exogenous thing to the economy, but cost is someone else's price, so it's not like exogenously costs change.

 

>> Bob Hall: The analysis that I presented earlier depends on a price called C, which is someone else's.

>> John Cochrane: If you say prices got more flexible because costs change more, that's kind of tautological cuz costs change more cuz prices got more flexible.

>> Bob Hall: There was no claim, this is not the result of running a regression where causation is an issue.

 

>> Speaker 28: If you see high cross-industry standard deviation of intermediate costs, you also should see more of this flexibility of prices at the same time.

>> John Cochrane: Kind of by definition, because the cost wouldn't be cheaper, costs are somebody else's price.

>> Speaker 28: You have more of these adjustments.

>> Bob Hall: Think of this as comparing two worlds, one subject to some force which has caused more dispersion in prices and therefore in costs.

It's just a question of do the endogenous variables follow the Description that I've offered or not. Excuse me, I was really surprised. Both aspects of this gave much, much more convincing results than I ever dreamt of getting when I started this project.

>> Bob Hall: Most of us struggle to get a t-statistic more than two.

If you're testing the hypothesis that one of these numbers hasn't changed, you get a t-statistic way better than two. Maybe I haven't understood.

>> Speaker 29: Just to get the story right, let's say it's 2008, Lehman has failed. You're saying something's happened which changes costs and then prices change in reaction to that?

 

>> Bob Hall: Yeah.

>> Speaker 29: And the thing that changes costs is, I mean, do you have in mind that there are demand shifts and therefore price changes? And going to John's question, those are the sources of the cost shifts, or there's something about factor productivity that shifted because it's a crisis.

 

>> Bob Hall: I'm just looking at data and looking for a relationship among endogenous variables. So it seems to me that it could be any one of many things, but they all converge. They all would have the same implication.

>> Speaker 29: Yeah, I mean, it's consistent that if input costs change, then output costs will shift as well by your model.

But then you just get wrapped up in this endogeneity how much of the cross-sectional price volatility that we're seeing is reaction to some fundamental underlying cost shifters, as opposed to reaction to other people that are changing their prices, and therefore a multiplier sort of effect.

>> Bob Hall: I don't see, I mean, I see what you're saying, and if I were running a regression or something like that, but I'm just looking at relations among endogenous variables and seeing a particular set up.

 

>> Speaker 29: Yeah, no, I get it. It's all consistent.

>> Elena: Just a question, following a little bit up on Daryl. So I've just spent a week talking to people from Princeton, NYU, of a different persuasion. They would tell you that we have a framework, a working framework for monetary policy.

That is the so-called Hank model, where the only issue is that the model is capable of producing countercyclical markups, but it has issues producing cyclical profits. And so I take their effort as being, you may or may not like it, but an effort that is overlooking a lot of the market microstructure, determinants of output and input price rigidities.

I'm very attuned to input market wage rigidities, labor markets. Shall I be thinking about your effort as one of opening the black box of the output market ones? Does that make sense, what I'm asking? You think of yourself as talking about this broad debate. We know that price rigidity are paramount.

 

>> Bob Hall: What's the broad debate?

>> Elena: The debate in Hank models that are models that are supposed to be used for monetary policy, but they have counterfactual implications about first order cyclical behavior of very relevant variables like markups and profits. But if you look at how this model-

>> Bob Hall: You're asking, does this approach blow Hank out of the water?

 

>> Elena: I'm thinking that if you open up the black box of those models, the way that output and input, market prices are determined, it's extremely primitive, if not counterfactual. And so I'm thinking about this effort of yours as going over the determined and surprised rigidities in output markets, which are critical ingredients in this mega frameworks.

Is that the way you're thinking about this exercise?

>> Bob Hall: Not sure. Well, can we talk about it later?

>> Elena: For instance, they have this Kabul rational structure where monetary policy doesn't have really feedback impact on how often you wanna adjust prices. In a world in which you do that in large industry, of course, you may want to do it differently because the effective price cost that you pay to adjust is different, a different level of the overall interest rates.

I'm just trying to think whether you're thinking about this as a model, one optimistic competitive model of the apple market for CEO's. It could be an ingredient into a grant framework monetary policy that is plausible at this level.

>> Bob Hall: There's a grand. Yes, okay, now you're getting into territory I recognize.

Do I have a grant of a new macro? Answer, yes, but I have to be cautious. And I would lose my audience if I revealed everything that's in my brain.

>> Elena: We can take it.

>> Bob Hall: Too many things that I would look like Roger Farmer.

>> Elena: So can we say there is a time varying cargo parameter, and you are trying to provide some micro foundations?

Why the Calvo parameter would be time varying in times of crisis, but then we don't know exactly how it happens. But this is where you're going.

>> Bob Hall: Yeah, yeah, so Calvo-

>> Elena: That's what I'm saying.

>> Bob Hall: Calvo loses his grip on prices when the pot has been stirred a lot, volatility is showing.

That's kind of a universal proposition. And so it can be lifted out of all the other ideas that I have, that are catching on, and promote that as an idea that may catch on.

>> Elena: And also more than that, cuz people will tell you, why bother with Calvo v Rotenberg, empirical, sorry, computational people, because the nonlinearities are very small.

Even if you have an entire distribution price to keep track of, you showed us linearities that are very important. So even those kind of statements are no longer true.

>> Speaker 28: I never liked Calvo because I knew SS. It's like, why do we have this fixed interval of time between price changes always?

I was not wrong because I knew SS. And so basically what you're showing is an example of why exactly SS is much better than- Either approximation. Calvo.

>> Speaker 30: Yes, one thing I agree with is this is-

>> John Cochrane: If you reset pricing, then you lose the Phillips curve. Is that-

 

>> Speaker 28: Well, Is that your agenda to save the Phillips curve?

>> Speaker 28: My agenda-

>> John Cochrane: Many have tried.

>> Speaker 28: It is to write down models that have coherent micro foundations as SS.

>> John Cochrane: As an empirical exercise in the history of economic thought, I thought the answer was reset pricing.

There's no Phillips curve. So we pretend that there's no reset pricing.

>> John Taylor: So, Bob, you wanna talk about-

>> Speaker 28: But with the lag, it's the lags that give you guilt But

>> John Taylor: just monetary policy, whatever, any policy issues.

>> Bob Hall: Well, let me finish. First of all, I've only gotten half of this.

So this is the quarterly cost data. TFP data is annual, which I I think is, okay. Okay, so productivity is much bigger lag in. So let me just show you the picture for, so it looks like we only have productivity numbers for the full year of 2020. And you can see that it's headed up, it's probably gonna go up some more.

The numbers will come out next month. So stand by for that. But it seems clear that we're seeing something comparable in magnitude in productivity. And that helps deal with the question we were talking about before. There is a natural metric of productivity. Okay, so the rest of us in the paper deals with.

 

>> Bob Hall: Okay, so it's very important to understand that these findings of volatility are not findings about a driving force of inflation. This isn't some new source of inflation that you haven't looked at before. It's something that should affect the monetary policy in particular, it should make monetary policy have more effect on prices and less effect on output.

So it would reduce the, right now the Fed likes this idea. That's how I end my footnote, the conference last Friday. Because the harmful effects on unemployment and output that would normally be expected for disinflation would be much much less in the world that I've described. Because we're still in an area where lots of firms are outside their zones of inaction, we're still in a relatively high volatility mode.

And that makes the Phillips curve, if you translate it into Phillips curve, basically works on the slope of the Phillips curve, makes Phillips curve steeper. Makes stepping on the monetary break, which we have been doing as an effective way to stop inflation and not pay such a high price in lost output.

 

>> John Cochrane: In your model I don't see a Phillips curve at all, how does raising interest rates have anything to do with inflation if this is how prices are set?

>> Bob Hall: Well, okay, so let's imagine one of the next steps is to recognize the heterogeneity and where firms are planted relative to their zones of inaction.

So some firms are very much in the interior and they're not gonna be affected very much at all. So they'll still contribute to the.

>> John Cochrane: But you said they don't react to demand. So there's no Phillips curve in this thing. So if I raise interest rates and that affects aggregate demand, that doesn't change anybody's prices in this.

 

>> Bob Hall: No, you're way off days.

>> John Cochrane: Am I?

>> Bob Hall: This is a model in which there is non neutrality of a Phillips curve character for some firms. Namely the firms that are planted well within zones of inaction when policy pushes all those firms somewhat, it's gonna get a Phillips curve effect.

So that's how this fits into.

>> John Cochrane: Is that written down?

>> Bob Hall: No.

>> John Taylor: Steven's question.

>> Bob Hall: Okay,

>> Speaker 31: I want to raise a different issue. You focus on volatility, but we know in standard SS Models that uncertainty widens the zone of inaction. And those same shocks you've been showing, the same episodes you've been showing us with lots of volatility, were also periods of unusual uncertainty by forward looking measures.

And that's a countervailing force to the one you've been emphasizing.

>> Bob Hall: Okay, well,

>> Speaker 31: so it's, so you actually, depending on which force is stronger, you could actually go either way. So think about the argument you just made with respect to the Fed. If zones of inaction on price setting are getting wider, then quantity responses would be bigger.

And that cuts, I'm not saying that's the right view, but it also comes out of this class of models.

>> Bob Hall: Okay, well.

>> Speaker 31: And it seemed to me you need to wrestle with that and argue if you want to, that the force, the volatility effect you're stressing is bigger than the uncertainty effect.

 

>> Bob Hall: Okay, we should talk some more and you should talk me into this.

>> Speaker 31: Okay.

>> Speaker 32: But going back to John's question, so monetary policy is gonna affect C?

>> Bob Hall: C has been pointed out quite a few times in this discussion is another word for a lot of prices.

We have to get into the question of how it is that monetary policy and the way it's currently implemented, how it has effects.

>> Speaker 32: Yeah.

>> Speaker 33: Well, you have a few.

>> Speaker 32: As you said, they're paying full interest on reserves. We raise the interest on reserves. Why does anybody in this model care about that?

 

>> Bob Hall: Because the way the Fed and like minded banks, which is almost all advanced economy banks operate. Is by setting two interest rates and confining all short term interest rates in the whole economy to that range, which is 50 basis points, right? So the central bank directly controls economic activity by changing short run interest rates.

 

>> Speaker 32: In this model, I don't see that anybody cares about the level of nominal short term interest rates. And if you even, you just said demand has no effect on prices.

>> Bob Hall: So, okay, well, okay, that gets us back to this.

>> Speaker 32: This is a serious question because I'm now looking for any such model and it's hard to find models where this actually happens.

 

>> Speaker 35: You have some slides on monetary policy.

>> John Taylor: You want to finish with your slides on Ms?

>> Bob Hall: I don't know. I feel there's such hostility.

>> John Taylor: Not hostility.

>> Speaker 36: A lot of model.

>> Speaker 37: I didn't mean it was personal.

>> Speaker 32: I just wanna see the rest of the model where raising an interest rate has any effect on anything in this model.

 

>> Bob Hall: Okay, well, this is just completely standard new Keynesian doctrine, which I think you're just expressing.

>> Speaker 32: Well, because you made fun of the new Keynesian Phillips curve, which is a central part of new Keynesian doctrine.

>> Bob Hall: Okay, but it involves things like the intertemporal substitution and consumption, stuff like that, right.

 

>> Speaker 32: Okay, so that would lower demand. And you told us demand doesn't affect prices in this model.

>> Bob Hall: The guy who's worked on models that seem useful here is for bill of Verdi.

>> Speaker 32: Yes,

>> Bob Hall: so he's got new Keynesian models with stochastic volatility. He talks about how that affects the transmission from monetary policy shocks to real and nominal variables.

That seems he was the very first person after this paper appeared on that to get in touch with me as a fellow traveler after this paper.

>> Speaker 32: Why can't you build on his models?

>> Bob Hall: Plus you can,

>> Speaker 32: or just take his models and run your thought experiments.

 

>> Bob Hall: Okay, but I was trying to lever, what I think is widely accepted in the macro community, even if you don't, if there's some aspects that you don't buy into. But intertemporal substitution in consumption and interest, sensitivity of investment. That's the sort of, that's the, that's the object that occupies the slot, the new Keynesian model that you don't seem to recognize.

 

>> Speaker 32: And then that goes through a Phillips curve to affect prices. But this model doesn't have a Phillips curve.

>> Bob Hall: Yes, it does.

>> Elena: So may I ask.

>> John Taylor: You wanna conclude.

>> Bob Hall: The rest of the slides would take too far, too long.

>> John Taylor: Another talk. Thank you 

>> Bob Hall: Okay,

>> Speaker 39: thanks, Barbara.