A Theory of How Workers Keep Up With Inflation

>> John Taylor: Very happy to have Erik Hurst speak to us today about, I don't know how you kept these titles, A Theory of How Workers Keep Up With Inflation.
>> Erik Hurst: We can talk after the end to see if that's the right title, but I think it's right.
>> John Taylor: I like anyway, welcome.

Welcome to be here, you have a big crowd. A lot of interest, and thank you very much for being here.
>> Erik Hurst: Thank you, it's great to be here. I've been here three weeks. I'm here through next Tuesday morning. So it's great to be here. So here's what I've been thinking about.

So what you're seeing here is jolts data on the vacancy to unemployment rate from early 2001 through, I think I stopped this picture somewhere mid 2024. And what you can see is the vacancy to unemployment rate increased sharply basically starting in the mid to mid teens, but really spiked 22 and 23 in the United States.

And this vacancy to unemployment rate has been interpreted that the labor market was pretty strong during this period where the vacancies are kind of the postings of the firms that they wanna hire. The unemployment rate is kind of the supply of labor. And people have interpreted that the demand for hiring was large relative to the supply of workers.

And that has showed up both among academics and policymakers as a kind of a conjecture that the labor market was pretty hot during this time period. Chair Powell has actually talked about this multiple times on reasons that they might have delayed cutting interest rates, keeping interest rates high because the labor market was still hot.

And then the belief is that the hot labor market would put upward pressure on wages and feed into inflationary expectations. Simultaneously, real wages were falling pretty sharply during this period. And so what I'm showing you here now is from the Atlanta Fed index, on average, this is median real wages in the United States.

I'll show you the whole distribution in a couple more slides using data from the CPS. And for those who are unfamiliar with the Atlanta Fed, they're just taking CPS data, tracking an individual over time, looking at Steve's wage today, Steve's wage one year later. See how Steve's wages evolved and then computing that for the distribution over time.

And during this period, real wages are still, this is again through July of 2024, about four and a half percent where they should have been based upon trend in the pre period. And we could talk about what the trend is here is a trend from 2016 to 2019, just kind of extrapolate.

We could talk about what the right trend is. But the key thing is real wages were falling during this period, still below some trend. And this isn't often associated with a hot labor market. Think about filing high vacancy to unemployment rate and a period with declining real wages.

And that's what this paper is gonna be about. And so we're gonna show both theoretically and empirically that the causation in kind of a modern macro model with a couple of realistic features. That the inflation itself can cause churn in the labor market, putting upward pressure on vacancies caused by real wages falling within a match.

And so that's what this paper is going to be about. And we're gonna kind of show a burst of inflation again. Where does inflation come from? We'll talk about that as we go through. But all else equal, could generate a sharp rise in the vacancy to employment rate again through this churn in a period resulting from a decline in real wages jobs.

Talk to me cuz there's gonna be lots of things you're gonna say, I'm gonna probably get you to tell me it's something that, okay?
>> John Cochrane: How much of that is just inflation and existing wages versus wages of new hires?
>> Erik Hurst: Yes, that's gonna be when you go through the new higher wages do seem to be moving more.

I'm gonna show you wage movements. So let me kind of tell you the kind of things that I'm gonna do. I'm gonna kind of show you a preview of results real quick. I'm gonna then show you just some data on the labor market along a variety of dimensions, not just these two that I showed you.

One of those is gonna be the wage changes of job switchers relative to stayers. And we could talk about some of that. That data I'm going to then set up and say can we generate that patterns both qualitatively and quantitatively in a model? I'm gonna write down, I'm gonna show you that.

And then I'm going to end by saying, well, what are other things that might have been going on during those period and how do those other things match these patterns that are going on? And then we'll end with, well then where did the inflation come from? So that's gonna be the kind of the game plan that we're gonna do.

But the first part of the talk is I'm gonna then kind of show you some patterns. But I wanna really gonna get down a theory and kind of say what is the implications of that theory when inflation comes along in a modern macro model with some realistic features.

And I'm just gonna trace out those implications and then we'll talk quantitatively stuff after that. Okay, so let me just give you a quick preview of the findings so you could kind of know where we're gonna end up. And then we'll get into the meat of the talk.

And I'm gonna show you that a temporary increase in inflation can cause a rise in the vacancy to unemployment rate, creating the appearance of a tight labor market without any other underlying shock. Just the inflation itself could do that. And the key is there's gonna be nominal rigidity on a match.

As the nominal rigidity on a match comes up, the inflation erodes your wages and workers are gonna take actions to escape that wage. Now in the model, as John already forecast, your outside option might be new hires or unemployment. How sticky are those wages is gonna be a key parameter in the background of kind of the model.

Now how is that gonna create vacancies through the lens of a model? The existing firms are going to post vacancies to replace the departing workers. But more importantly, when there's lots of people switching, it's cheaper for firms to hire a worker, all else equal, because they can match with a worker quicker.

And so you're gonna get this burst in vacancy creation as a result of this. A lot of it's just gonna be churn of like musical chairs in the labor market. Ellen comes to Chicago, I go to Minnesota, and there's no really change in the underlying unemployment rate from this.

So you're gonna get a rise in churn, a rise in vacancies without any underlying change in the unemployment rate. And then I'm gonna show you calibrating the data using pre-2000s data, shock with the inflation we observed. And I'm gonna show you a quantitatively and qualitatively matches a lot of the patterns.

I'm gonna start motivating in a few slides, both in the aggregate and the cross section cuz there's gonna be a distribution of.
>> Speaker 5: So this is consistent with a story that firms post in this recent period. They posted vacancies even when they didn't really have the position just in expectation.

Yeah, all of that would be consistent with all of that.
>> Erik Hurst: Exactly, exactly. And I'll show you that as we go through. Once we get the model up, you'll see kind of what the firms are gonna be doing, yeah. How do we get it?
>> John Taylor: In the 1990s, unions had cost of living adjustments, and they got rid of those in the early 2000s.

And as a result, now you're getting a lot of strikes with workers trying to catch up for inflation. Is that embedded in the model or.
>> Erik Hurst: Do you have the strikes in the background? But let me tell you on my fourth point, I'm gonna give you two other things.

First to kind of tell you what I'm gonna do. And then the fourth point is going to be related to workers are going to hate this and it's going to give us some rationale. To understand what has been going on with workers in the labor market in the recent period.

>> Speaker 5: But inflation has to be high for a long period of time.
>> Erik Hurst: In the model the expectation process is going to be important. And you'll see that once we get the model. So I'm gonna defer that once we get to actually quantifying the model, we're gonna have to take a stance on some of those things.

I'm gonna show you the model first, but Anna's question is gonna be exactly. It's gonna be a parameter, the persistence of inflation is going to be an important to turn some of this thing. So the second thing, and this is my favorite part of the paper, I'm gonna then explore historical data.

I'm gonna get to this towards the end and I'm gonna show that in prior periods of inflation in the past, like 1951, related to the periods that Valerie, right after Valerie Sample ended from her talk last night. 1974, 1979, you saw again a very large spike in the vacancy to unemployment rate in a period where the labor market looked weak on other or not particularly strong on other dimensions.

And I'm gonna show you that inflation systematically seems to be a shifter of the beverage curve, the relationship between the vacancy to unemployment rate and unemployment using historical data over time. I'm gonna end with the last, last thing I'm gonna say is that other stories that are out there working from home, sectoral reallocation, productivity shocks, traditional demand shocks are gonna struggle to match collectively many of these pieces of the data.

The real wage decline is gonna be one key component, but there's gonna be lots of other metrics that these other types of shocks are gonna fail. And then the last one, and this is what I'm gonna do in the middle part of the paper, I'm gonna provide a model driven reason why workers dislike inflation.

With the only other friction being in the model nominal wage stickiness on a match. And then I'm gonna show you that the recent inflation reduced welfare of workers by about, we'll call it one month's wage. Okay, a little bit less at the bottom, a little bit more at the top, and then I'm gonna decompose where those welfare gain losses are gonna be coming from.

Some of it's just the real wage erosion itself, but workers are gonna then take these costly actions to help escape these nominal wage rigidities. So we got to keep into account the search costs. And I'm gonna call this other thing a renegotiation cost when we get into the model.

But there's also gonna be gains that are gonna be around there as well cuz firms are gonna be moving workers away from the layoff margin because they're relatively cheap. And so you're gonna get some gains from reduced layoffs through the lens of the model. And so I'll be able to quantify each of these components going forward.

>> Harold Ulugh: Surprising that labor contracts aren't indexed
>> Erik Hurst: In some countries they are when inflation is a lot more common. And so then we're gonna have to think about, once we get to the model, how permanent this is. There's gonna be a parameter in the model that might adjust into the indexing endogenously.

And I'll show you that once we get into the model details.
>> John Cochrane: And they may be again. Well, another thing people have talked about here is differences between workers. A dean once said inflation is the dean's best friend because the people who move are the one are the better workers.

The people who don't are not so good workers. So in some sense it's a wages start shifting to marginal product, but people collecting on old promises get screwed. Is that-
>> Erik Hurst: I mean, you're gonna have some of that in the model. We're gonna have some dimensions of heterogeneity, we're gonna have some productivity level.

The different parts of the distribution are gonna naturally churn a little bit more than others. So the old embedded professors, we don't move too much. And so the costs on us are gonna be more because we're not gonna be able to easily escape the real wages. So you're gonna get some wage compression during this period.

Everybody's wages are worse off, but the bottom is gonna be less off, worse than the top to the lens of the model. And that'll be a lot easier once we get the model on the table. So you can see kind of the.
>> Speaker 6: Story about manager inflation, being the manager's best friend is about downward nominal stickiness.

You've got upward nominal stickiness here too.
>> Erik Hurst: Yes, and so the model is gonna be asymmetric. So who could then put in different shocks within the model.
>> Speaker 6: This is very different from some Keynesian stories that would emphasize downward nominal rigidity and upward.
>> Erik Hurst: Still, the intuition from John's comment is still gonna be there that firms are making lots of profits during this period.

So I'll show you, you're gonna get firm profits going up. And in the data we see historically high firm profits in the same period as well. And we saw them those high profits in 1974 conditional on the state of the economy. We saw the high profits in 1951 conditional on the state of the economy.

So we are transferring resources during this period. The real wage rigidity is a transfer from the workers to the firms during this time period.
>> Harold Ulugh: It's transfer you wouldn't get the labor churn, right? Because people that are productive, they would just renegotiate to the current employment.
>> Erik Hurst: Exactly, so both of those margins and so both of those things are gonna be trade off for different types.

>> John Cochrane: You need a story that they can't raise your salary without raising my salary, so you got to go get a job.
>> Harold Ulugh: Well, but then you have the upward rigidity too.
>> Erik Hurst: We'll see again once we get in the model, we can have this discussion a little bit more.

Let me just kinda summarize the three big takeaways and let me go to the data, yeah.
>> Speaker 7: So why do you ever in this world, like why do you have rigid contracts at all with labor?
>> Erik Hurst: Yeah, why nominal wage rigidity is there? There is contracting frictions in the world.

Once we get into the bottom, there is contracting frictions in the world. And once I show you kinda what we're gonna assume, then we could talk about the realism of those. And I'm gonna show you data that's gonna help us discipline kind of this component of the real world.

Yeah.
>> Speaker 8: I mean, one way to think about it is every time you're bargaining in the labor market, adding another state variable is costly in terms of the amount of time you have to bargain. And it's actually a testament to the previous success of the Federal Reserve at staying close to the 2% target that they took these out of the contracts and then that's why it was so shocking to have the high inflation out.

>> Erik Hurst: But if it was permanent, then maybe our contracting rules would change back to Anna's question going onwards. And that's gonna be, you'll see that when that comes into the model when we come through. Okay, so three, there's a high level stuff. Policymakers and academics should be cautious about viewing the rise in the vacancy to unemployment rate as a sign of a hot labor market during inflationary periods without looking at other moments of the data.

The high additional real cost of inflation that arise through highlight the additional real cost of inflation through the labor market. Again, the search costs and renegotiation costs are gona be things maybe our models wanna take into account. And it's gonna provide, and I think many of you are already moving in this direction, a model based reason why workers report disliking inflation so much during the recent period.

It shows up in surreys, it shows up in post election results. There's a whole bunny types of moments where workers were seen to be very dissatisfied with this labor market in recent periods. Now I'm gonna show you a handful of data just from public sources to kind of get some additional moments on the table that we might want theories to potentially explain during this period.

I'm gonna show you a series of pictures like this. All of them start in 2016, January, and they all run through mid to late 2024, depending upon the picture I'm gonna be showing you. The shaded years is what I'm gonna call the inflation period that's going to run from April 2021 through May 2023.

And it's any time in the US just by a rule that the inflation rate was above three and a half percent. So, that is a period where it crossed three and a half percent and then came back down under 3.5%. There's gonna be two lines on these figures, one which is gonna be the average of the data from 2016 to 2019, pre-pandemic.

I'm gonna throw out, 2020 and early 2021 and all my analysis. So the pre-pandemic trend and then the trend during the inflationary period. The first pictures I'm showing you are just from jolts. There was a huge decline in a historical sense in the layoff margin during this period where the layoff margin has declined by about 20% relative to the 2016-2019.

We see a big movement in the quit rate during this period. Many of us in this room have been talking about the quit rate in various different types of models. The quit rate was elevated, it's coming back down towards trend in recent periods and the vacancy rate jumped and is still coming back towards trend but still elevated relative to the 2016 and 19.

>> Harold Ulugh: Okay, think about the total labor force.
>> Erik Hurst: Yeah, I'm gonna show you two slides, Harold, exactly. So Harold's already gonna be after this one. I'm gonna show you a labor force side going through from these two periods. So this is gonna be the worker side.
>> Pete Klenow: The last point about in all industries.

>> Erik Hurst: I forgot to mention that.
>> Pete Klenow: Yes, so I would have thought there'd be some industries who are stickier wages and. They would have a bigger increase in vacancy rate.
>> Erik Hurst: Yeah, I think, but as we talked about earlier, those manufacturing kind of things, those indexing unionized contracts, have gotten less and less components during this period.

So the vacancy rate did move sharply in all industries. So the vacancy rate on average increased by about 50% if you take that 4 to a 6. All industries from the jolts range from about 40% increase in vacancies to about 80 in most indices, except non-durable manufacturing that jumped by about 100% in the vacancies.

So almost every all had substantial increases. There is variation across the industries. To a first order, every industry had one of these big increases. When we start thinking maybe stories of sectoral reallocation we should keep this in mind. These are patterns are relatively broad based. This is the worker side flow of those analysis.

So now this is from CPS data and I'm going to measure job to job flows in the CPS and unemployment to employment flows in the CPS. You could see that in the period when the quits were running high, there was a lot of E to E flows occurring in the data.

There hasn't been much at all change in the U2E margin during this time period. So the churn is coming or at least the looking of the hot labor market is coming in churn, not so much in changing the propensity for those unemployed to enter into the labor force.

And again, these occur for all groups of people. But there is more churn during this period even relative to the pre period at the bottom of the distribution relative to the top. The top churns, the bottom turns more. This is Harold's question on just trends in the employment rate in the pre-period and the inflation period.

Nothing changed on average. So there wasn't a big change in the unemployment rate. There wasn't a big change in the employment rate compared to the 2016, '19 in the inflation period during this thing. You get a little bit for women with a bachelor's degree or more, but that's part of a secular trend if you even take that out 20 years prior.

But all other groups were relatively constant. But let me show you, I mean.
>> Josh Raul: It's a small point, but people did get older in this period, and pre-pandemic projections were that the employment rates would be falling for many of these groups because just retirement. Yeah, so.
>> Erik Hurst: And again, I should be fair.

I'm showing this picture for 2020, '25 to '55. It might make better, maybe the flows are going to be for the whole economy from the firm side. Maybe I should think about doing it for the whole group.
>> Speaker 8: Because there was a lot of retirement, you know, around COVID.

>> Erik Hurst: Yeah, but that's in the COVID period. So now this is again, we're now thinking about the inflation period per se cuz all of these patterns really were peaking in 2022 and the employment rate and the unemployment rate were back. But there are these secular prime age restrictions.

>> Josh Raul: So that largely addresses.
>> Erik Hurst: Yeah, but I think your point is maybe I shouldn't have the prime age in this one. Let's take a look at the total thing. I should at least look at that, this is just prime age. Let me show you now from the Atlanta Fed data, just the distribution of wage changes at the top in the bottom of the distribution, and it's monotonic for the other quartile.

So I didn't even show you those. You can see those in the paper. But the bottom of the wage distribution is about 2 and a half percent below trend where the top is about 7% below trend in terms of this period. So everybody's below trend but there is wage compression during this period and there has been some papers.

David Autor has some kind of things about wage compression during this period. He's talking about a hot labor market because he's looking in nominal kind of sense, but in real terms, everybody's wages are going down, but they do go down less at the bottom than they do at the top.

This is wage rate. This is wage rate, right from the CPA. Yes, so this is basically hourly earnings. If you're hourly and it's weekly earnings divided by usual weekly hours. If you're selling, yeah?
>> Michael Boskin: Price index using.
>> Erik Hurst: I'm using the CPI for everybody. So again, if there's differences across groups, that's outside my model.

And you should adjust all of that by this.
>> Michael Boskin: Saw a lot of bias over five or six years.
>> Erik Hurst: Again, that will affect levels, but not the distribution and kind of bone it unless people are. You wanted to deflate by different people, right?
>> John Cochrane: So like I get a picture that, the old established tenure professors take a hit.

The younger system already, the way they don't. That it's not really about where your wages are, it's about where you are.
>> Erik Hurst: Yeah, it's about the churn. And I'm gonna show you there's going to be some links between your wage and the churn. But John's already got the model mechanism that's gonna come out of this.

Different parts of different distribution are gonna have different propensities to churn and that's what's gonna drive these patterns in our model. So we're gonna be able to match that through that mechanism that John just outlayed. Okay, let me show you one last one, cuz there's again another moment that we want the data to potentially match.

What I'm showing here is ADP data just from their website. They've kind of taken the stuff that me and John Grigsby did in our AR piece, and now they've kind of putting it out on their web page for everybody to see. This is the average nominal, I haven't deflated these, nominal wage of job changers, the top line and job stayers, the blue line.

And that initial period gap is kind of what John and I got from 2008 to 2016 average. The job stayers kind of change about 2%, job stayers about 2%, the job changers about 6%, about a 4% gap. That gap exacerbated greatly during the recession. So the wage change of job changers increase disproportionately more the than the wage change of job stayers during this period.

And it's kind of moving back towards pre periods late into the period. Again, you get very similar patterns from the Atlanta Fed data as well. So a lot of the wage growth is coming from job changers, that always happens. But even disproportionately more.
>> Erik Hurst: It is individual fixed effect of workers.

So it's Harold's wage growth.
>> Harold Ulugh: 16% in it means that from-
>> Erik Hurst: Year over year. Sorry, year over year changes. I'm sorry, Harold. Everything's year over year change. So this is annualized growth of wage change for job changes.
>> Josh Raul: And say similar patterns in the wage tracker. You mean just for job stayers?

>> Erik Hurst: And job stayers if the gap doubled, the levels are gonna be.
>> Josh Raul: Tracker just follow stairs, right?
>> Erik Hurst: Notifiers changers who stay in the same house. If you go to the Atlanta Fed now, you could click on a button and there'll be exactly that picker. But Steve's point, the magnitudes are a little because a lot of the job changers get missed from the CPS, particularly those who move house.

And those tend to be more selected. And so you see the same patterns muted in the Atlanta Fed, I mean relative to the ADP data. And that's why I'm showing you this one. Okay, the background of models that we have during this period. Here's some data that we might wanna match E to E transitions increase sharply, not much in the UDE rate.

Real wages fall sharply have been catching up slowly disproportionately declines at the top relative to the bottom. Real wages of job changers increased much more relative to trend compared to job stayers and vacancies increased sharply. But unemployment was relatively constant. We're getting kind of shifts in the beverage curve during this period.

So that's kind of the background. Now I'm gonna come and just kind of play with the model for a little bit. We could write down these assumptions that all of you wanted to kind of get to and we'll kind of formalize kind of those assumptions. And then we'll play quantitatively after where we'll see, the quantitatively is gonna more proof of concept on some dimensions.

We'll at least get understanding the mechanism of the model that we want to cover.
>> Pete Klenow: So Erik.
>> Erik Hurst: Yeah.
>> Pete Klenow: I'm guessing you're not going to have this in the model, which is that suppose there's some workers who are a bad match and the firm doesn't feel like it could cut their nominal wage back to Steve's comment.

This might be good reallocation from a productivity point of view for the firm to get rid of them rather than offer them higher wages.
>> Erik Hurst: Yes, in one dimension. So if the workers productivity attrits over time. Let me kinda show you what that's gonna be in the model.

Once I show you the model we could kind of see what's missing. But we're gonna have a force of that. We don't have any reallocated effects of churn in our model. But we are going to have worker types sometimes being bad workers wanting to be fired. The firms wanting to fire them or cut their wages, but because of nominal rigidity, they might fire them.

We're gonna have those mechanisms and that's gonna be when the layoff margin is gonna be moving. That's gonna be some benefits to the economy from that. So we're gonna have some of that. But to Pete's point, I'm not gonna have any sort of match specific, fit between workers.

I'll show you the product. It'll be easier once I show you the production function. But we're gonna have some of the essence of Pete's comment in the model. So let me kind of show you the model and then we could talk about what it might be missing after that.

Okay, so we're gonna have a model of labor market flows. It's gonna be relatively standard with two additional frictions. The first, there's gonna be frictions and nominal weight adjustments on a match, okay? It's going to look, I'm gonna show you, when we specify it's going to have a calvo and menu cost flavor from New Keynesian models.

I'm gonna have both aspects in there and I'll show you why I need both aspects into our regular search and labor matching models. The second component we're gonna have is there's gonna be a lack of commitment on the part of workers and firms. So you're sometimes going to get, because of these nominal wage rigidities, some inefficient transitions.

Some workers are gonna be fired and some workers are going to quit. Not everything will be renegotiated on the match. We're gonna have endogenous worker flows in the sense that workers are gonna be able to quit to unemployment. Firms are gonna be able to lay off workers and you're gonna have job to job to flows.

I'm gonna have some exogenous shocks in the model that are also gonna exogenously attract workers. I already told you these frictions are gonna apply that some of these flows are going to be inefficient. There's gonna be heterogeneity and worker type across the model. They're gonna differ in a bunch of dimensions, which I will specify as we go along.

There's no heterogeneity on the employer side, so there's just gonna be homogeneous firms in the background. I'm gonna tell you the game I'm gonna play and then we'll come back and relax this afterwards. I'm going to have God just a changing the inflation rate as a shock in the background of the model.

Okay, you could think about as a monetary policy shock or something else going on. I'm not gonna microfound any of that. We will talk about where the real inflation might have come at the end of the talk and how that might interact with some of the patterns. But right now the game I'm gonna play is just an exogenous change in the inflation rate and trace out how that's going to move on worker flows.

>> Harold Ulugh: Maybe it was a devil changing inflation.
>> Erik Hurst: May not be the gut, it depends on your rate. But yes, the model could be anything. So once we get to the model, we could then trace out, as Anna said before, whether it's permanent, whether it's temporary. Whether it occurs on a Tuesday all at once, or whether some of it's on a Wednesday and some of it's on a Thursday.

All of that's gonna be important.
>> John Taylor: With the institutional rigidities, you include lags. For example, unions lose because they're stayers, but they make up for it in the second period.
>> Erik Hurst: Let me show you what I have and then we'll come back and say what we could potentially add in addition to what I have.

Let me kind of get to the guts of the model now. So now I'm gonna kind of start to show you some notation and some equations to kind of formalize what I have. And then we can kind of see what is missing and what might be valuable to add for the questions that I'm trying to address.

So time is gonna be continuous, workers are gonna physically die at an exogenous rate. They're just gonna leave the labor market. Workers are only gonna have two states at any period of time. They're gonna either be employed or unemployed. I don't have a three state model, there's not a home sector.

So everybody's either searching or employed. We're gonna have heterogeneous worker productivities. So all of us are gonna be born with some initial, I'm gonna call it level Z. Some of us are gonna be high Z, some of us are gonna be low Z. It's gonna come from some log normal distribution at birth and then it's gonna evolve there thereafter with some Brownian motion with drift.

So some of our productivities are gonna go up over time. Some of our productivities are gonna go down over time and the drift differs between whether you're employed or unemployed. So for those of us employed, maybe our productivity is increasing on average over time. For those of us who are unemployed, maybe our productivity doesn't increase as much.

Our production function is gonna be very simple. The output from the firm I'll just call X here is just going to be a common aggregate productivity At times the workers productivity Zit. I'm gonna normalize A to 1 and everything I show you. But when I do counterfactuals with productivity shocks later on to see if they can match the data, I'm gonna shock that a thing up and down.

In terms of notation, capital W Tilde is going to be the nominal wage W Capital W is gonna be the real wage. The nominal wage deflated by some price index P. That's what God is gonna come and change. And there's gonna be some markdown which I'm gonna call little W hat, which is going to be your log productivity minus your log wage.

Where is that markdown gonna come from? Everywhere in the standard search model, firms are gonna have to recoup their job posting costs. So your wage is gonna be a little bit lower than your productivity in the background. The nominal rigidities are also gonna move this thing around.
>> Josh Raul: On average, your wage is lower than the product.

You're gonna have some workers whose weight because yeah, okay.
>> Erik Hurst: We're going to have a distribution of market.
>> Josh Raul: Okay, from the facts that you showed before, don't we learn something about the distribution of that markdown or markup? I mean, it seems like when inflation happened, pretty much everybody took some real wage, which suggests that there might have been a lot of people out there whose wage was higher than their productivity.

>> Erik Hurst: It can't be too high cuz then the firm will fire you at some point. So you're gonna be capped on how high your productivity is. So we hired Josh. Josh's productivity is going up somewhat. In this case, Josh productivity is going up. His nominal wage is fixed.

He's gonna quit and go try to search at another firm or renegotiate with his existing firm. So there's going to be endogenous quits, these endogenous fire. If Josh's productivity goes down too low, your markdown, is gonna be limited cuz the firm is gonna fire you at some point.

So there's gonna be a distributions of markdowns in the data which is gonna have some bounds because of these endogenous quits and inquiries. That's exactly the model we're gonna build. Okay, let me tell you the other parts of the model. There's gonna be a home sector in the background, for those who don't work, you're going to get some utility B.

That utility B is gonna potentially scale with your productivity Z in some arbitrary way which I'm gonna call phi B, which we're gonna let the data tell us what it is. What is phi B? If phi B is less than 1, it means that lower productivity employed workers are gonna be on average closer to their outside option.

And so they're gonna hate unemployment less than the high skilled worker B less than 1. I'm gonna estimate from the data. So that's gonna be the relevant case. But it could be anything. It could have been greater than 1. Which means the high productivity workers like unemployment more on average than the low productivity.

That's gonna be one form of heterogeneity in the background, John, that's gonna help explain differential churn at different parts of the distribution across workers. We're gonna have firms in the background. There's gonna be directed search where firms are gonna post some vacancies offering a real wage. And the real wage is gonna be associated with a given productivity Z.

So firms are gonna post a vacancy and say hey, this is the vacancy. If you come Z type, you're gonna get this wage. The cost of posting a vacancy is gonna be K or kappa, I forget what I'm using there. And it's also gonna scale arbitrarily with your Z.

It might be more expensive to hire more productive workers than it is to hire low productive workers on the part of the firm.
>> Josh Raul: How is the incidence of their posting costs on? That's not obvious, maybe it's standard.
>> Erik Hurst: I mean there's going to be an equilibrium where firm is zero profit firm condition on terms of entry that firms are then going to want to make sure that on average they're earning zero profits in expectation.

And so that means the wage is gonna have to be the cost that they have to bear is going to be an equilibrium have to be recouped somehow to get the zero profits. So that is standard in this kind of living. I'm also gonna estimate in the data later on that it's gonna be look like through this lens of the model more expensive to hire high types than it is low types.

So the PK greater than 1 is what the data is going to spit out. And I'll show you how the data is gonna spit what moments are I'm going to infer this from in a few slides. I'm not gonna talk much. Everything here is relatively standard. There's gonna be a Cobb Dougling matching function in the background where firms and workers are going to meet and match with some probability.

The only two things I wanna flag in the background we're gonna have a search function. Workers are gonna spend some time searching. It's gonna be utility cost. I'm gonna specify that in the next slide formally but the cost is gonna be a function of both their productivity and the state.

It might be more or less costly for unemployed workers to search on average than it is for employed workers or vice versa.
>> Speaker 8: So you say you have an exogenous separation shock, but are there also endogenous separations?
>> Erik Hurst: The whole model is endogenous. So on top of it.

So we're gonna then allow one more margin to help fill the data. There's also gonna be some exogic, God's gonna also come down and just kill some matches from time to time. Everything else is going to be endogenous for exactly what my answer to Josh was before. So we're gonna have both endogenous and exogenous flows in this model.

So let me just summarize. The workers are gonna differ in productivity. That difference in productivity is also gonna imply differences in the value of non employment. The way I've specified differences in potentially the cost of focusing a vacancy. Potentially differences cost and search and these exogenous separation rates we're also going to allow to differ by type that is the heterogeneity on the worker side in the model.

All of them are gonna be functions of this 1 Vector z your type at any given point in time. So here's preferences and I'm gonna unfold this slowly over slides. So what are workers gonna get utility over? They're gonna use their wages to fund some consumption. Anytime they search they're going to have to pay a utility cost of search.

And if they so desire to renegotiate with their boss, as Harold said earlier on, they might have to pay a cost of that as well. I'm gonna spend some time talking about that renegotiation cost in the next few slides. But this is going to be the way workers could escape their nominal rigidity.

So they have these two margins. They could do costly search or they could have some renegotiation. And I have to tell you a lot, and this is the guts of the model now about what is allowed for free and what is coming with a cost as we go through the model.

In order to do that, I'm gonna have, let's say, a relatively complicated wage adjustment process, but I'm gonna have a wage of adjustment process with both a calvo and and a menu cost component. Why am I gonna have both? I'm gonna actually show you the data first and then I'm gonna kind of use the data to motivate why I'm putting in both of these forces through the model.

And I think it'll be clear when I go through the next slides why I'm gonna need both. But this is a figure from my paper with John Grigsby using the ADP data. And so this is going to be the year over year base wage changes for individuals in the economy and for those unfamiliar, ADP is about 20% of the US labor force is in the ADP data.

So this is 20% of the US population, relatively random. We do a lot of work in this paper that say this matches well the representation of the aggregate economy along the dimensions associated with wage adjustments. As we've seen people have alluded to before between 2008 and 2016, there's essentially no nominal wage cuts.

It's not zero, but essentially nominal. It's about 1 or 2%. So there's gonna be some asymmetry in the data, at least in terms of potential in terms of costliness of wage adjustments. There's a huge spike at 0, a large mass of workers who kind of change between 0 and 2% and then a drop off and then some tail of adjustment after that.

So, the model of wage adjustment we're gonna want is you're gonna want to have basically hard to get 0, less than 0, a big spike at 0, a lot of mass between potentially 0 and 2 or 0 and 3% and then some tail after that. So I'm gonna have two forces that are gonna help me match this kind of distribution.

Let me tell you what those forces are and then we could see why we need both or quantitatively what they're doing as we go. So here's the first part of the wage adjustment. So we're matched with a firm on the match, nominal wages are fixed. A Calvo ferry comes down every once in a while and taps you on your head.

And when the Calvo ferry taps you on your head, you get to adjust a part of your wage for free. You don't have to pay any sort of renegotiation cost or search cost. So your nominal wage is fixed until the Calvo ferry taps you on the head. When the Calvo ferry touch you on the head, I'm gonna call that arrival rate of lambda.

You could adjust your wage from anywhere between 0, and we'll call high W bar for free. 2%, 3%, whatever it is. Now this could be based on norms. This could change with the permanency of the shock. Right now I'm just gonna have it as a fixed number, but this is gonna be what you can get for free from a nominal wage change.

So when the Calvo ferry taps you on the head, your wage could change anywhere from 0 to 2%. If the NASH bargained wage is greater than 2% or PI W, I'm gonna set that to 2% in the model. If it's gonna be greater than 2%, you're just gonna get 2% for free.

And then otherwise, if it's less than 0, you're just going to get 0. And if it's in the middle, you're just gonna go to the Nash bargained outcome. Now, what this does is it gives you kind of a range of wage changes that you could just get in a normal Calvo component.

So when Booth changed my wage in the middle of the recession, I got my usual 3% growth despite the inflation rate being much larger. What did I get the year before? I got like 3%. What did I get the year before that? 3%. So there was some part, except when Steve was dean, I got like 2%.

But in normal minus two, it was at zero. So there's downward stickiness. And so, there is something about this is kind of representing the norms in kind of wage setting that we tend to see that kind of come through normal wage adjustment processes.
>> Speaker 5: Because otherwise with the cost for negotiation, you would expect negotiations to happen less often, but be larger.

And that's not what it seems like the data shows.
>> Erik Hurst: Exactly, and so that's gonna be the next part of where we're gonna get is now there's gonna be this renegotiation cost which is gonna come with more frequency when the inflation rate is higher, when nominal wages are going to see it.

>> Harold Ulugh: But there are lots of bits and pieces here like this one and that firms can fire and other things that it's not entirely clear to me which ones are really essential for the main.
>> Erik Hurst: Yeah, so I'm going to hopefully, when I get to the quantitative stuff, at least I could show you quantitatively what things are.

>> Harold Ulugh: This one is that trust there to get a little bit of a wage dispersion.
>> Erik Hurst: It's not only give you wages, it's gonna reduce the cost of inflation, and so in normal periods of time, the cost of inflation isn't that big. So when it's 3% or 2%, it's not really creating additional churn in the labor market.

People know that they'll be able to do it. So what it's doing is giving you some wage adjustment for free when inflation comes. You could take this to zero and then the cost of inflation becomes even greater during this period.
>> Harold Ulugh: Would have just been to say wages go up to bar W for everyone and rather than putting in the coal ferry and then wages doing low inflation episodes would just go up by regular inflation.

>> Erik Hurst: And that would be great if that did that. If we saw that in the data, the data seems to reject that. And so that's why I said this is a quantitative point.
>> Harold Ulugh: That's another feature of the data.
>> Erik Hurst: And then the action is then gonna also come in inflation periods through the second part.

So in the second part you get the Calvo ferry for free in the first part. And then when inflation is high now, you're gonna have to take some costly actions. And so churning is gonna be one, we'll talk about that. But also you might be able to walk into Steve's office when he was the dean and kind of say, I'm going to start looking around or I went out and got an offer someplace and maybe you wanna match it.

And I have to take some costly action either with the capital in the dean's office or my search to bring them back an offer that allows us to do some renegotiation. And so what is that gonna look like? The cost of renegotiation is gonna be drawn with some distribution that's gonna allow me the cost that I'm gonna have to pay.

So some of us might be able to renegotiate for free and others might have to renegotiate in a more costly sense. So now if in a high inflation environment, you get your 3% for free, but if you want more than 3%, you're gonna have to take a costly action with fee being the cost.

I forget which one that is, pitchfork being the cost that you're gonna have to pay. Yeah, Poala.
>> Poala: So in the data, is it true that the people with low skills, because in some way we know that they catch up more and there were more vacancies there. Is it true that they were either the disadvantage, they had more stickiness or.

>> Erik Hurst: They churned more so turned to churn more. So I didn't show you that I should have had that in the thing. Yes, exactly. Yeah, I calibrate the model in a pre period and they're gonna be because they churn more through the lens of the model, they get to basically adjust easier and that's how their wages keep up more than the top of the distribution.

>> Poala: So just to see some of the changes of your models, if there was no shock, there is no macro shock and God doesn't change it. Does your model match some of the features of the data where for example we didn't have any macro any monetary shocks.
>> Erik Hurst: We're gonna calibrate to match all of those kind of periods in terms of the wage distribution and the worker flows.

And so we're gonna use the pre periods worker flows and wage distributions to calibrate the model. So we are going to match that wage distribution or some parameterized version of that wage distribution and the worker flows by design. Okay, so I'm gonna pick parameters to match that and then I'm gonna shock the inflation, see what the model predicts and then I'm gonna compare those predictions to what the data actually did.

So the game I'm gonna play is how well quantitatively does this calibrated model to match the wage distribution and flows in a pre period actually match the wage distribution and flows during the after the inflation shock. Again, just a one caveat Steve or you know I kind of shut down all the asymmetry in the paper.

I just made sure there was no wage cuts. In the kind of slides I'm doing in the paper we do allow for another its distribution of pitchforks to occur if you wanna cut the wages to match the 1% or 2% of wage decline. So in the paper we're more precise than what I'm doing in the slides just to provide.

>> Speaker 13: May not be within the norms of what is behavioral and accepted and what is a fairly shock and accepted but you have this whole cohort inflation expectations. So when you'll get shocks and what do I expect in terms of persistence of those shocks and permanent could be cohort dependent.

Did I see inflation? Did I not see inflation? Is that not in this but like are you thinking about that?
>> Erik Hurst: I mean I think this is Anna's question early on the expectations of the inflation shocks are going to be immensely important in the paper. Now the one thing you think about when the inflation shocks are going to be more and more permanent, you might want to endogenize that pie bar w what you get for free.

If we go to a scenario where steady state inflation rate is is gonna be 10 forever. Harold said maybe we just get 10% for free. Whoever as part of our bargaining contract.
>> Speaker 13: I'm thinking more about cohorts are more.
>> Erik Hurst: I don't have cohorts in the model. So it's basically just everybody is gonna be a steady state on there.

So I don't have that cohort.
>> Speaker 8: Decision to become educated.
>> Erik Hurst: Exactly.
>> Speaker 8: Very much a function of that.
>> Erik Hurst: Exactly.
>> John Taylor: Step on melody, those kind of things.
>> Erik Hurst: And again the more you wanna do permanent shocks, I think the more these things become interesting in this period.

Financial markets at least thought they were gonna be temporary. Workers thought they might be temporary. I'm gonna use temporary shocks to actually just, as our baseline that I'm gonna use to evaluate the model quantitative. They did too, no, exactly. Okay, so let me kinda summarize the rigidities, and I think John hit one of these early on.

I just want to formalize it. What I'm gonna do in the paper right now is the new higher wage is gonna be perfectly flexible, and there is some evidence that they are more flexible. The key part is the qualitative predictions of our model will go through as long as new higher wages are slightly more flexible than existing matches.

But the quantitative stuff I'm gonna do, I am going to assume that new higher wages are perfectly flexible. And I'm also going to assume the value of the home sector is also in real terms. The value of leisure, that's a big part of not working, is gonna be in real and not in nominal terms.

That second one really just affects the UE margin, not so much the ED flow. Okay, yeah.
>> Speaker 14: Are you done with the model?
>> Erik Hurst: I'm done with the model.
>> Speaker 14: So you didn't talk about budget constraint, you didn't talk about assets, transfers or any of these things. Are they gonna play any role?

>> Erik Hurst: If there is a budget constraint. So the C that is going to be in the model is going to be based upon your permanent income. You're gonna forecast what your costs are going to be. So I should have put the budget constraint after this. But there is a budget constraint that is going to be bound by the households that are going to fund their consumption in each period.

The workers are going to be forward looking. So it's gonna basically going to have some-
>> Speaker 14: Save.
>> Erik Hurst: Yep, they could save. Yep, yep.
>> Speaker 14: Everything adds up.
>> Erik Hurst: There's no government in this model so I don't have to worry about the government adding up in this model.

But for the household things they can save in terms of some of their shocks into consumption smoothing, all of that's going to be orthogonal to the unexpected. Inflation, reducing real wages. And that's gonna be the shock that's gonna come through, yeah. It's an MIT shock, I should have said that.

>> John Cochrane: It's a immense and nasty model.
>> Erik Hurst: Yes.
>> John Cochrane: Value dynamic with this value function.
>> Erik Hurst: You wanna see the value functions?
>> John Cochrane: I'm hoping for the Minnesota definition of equilibrium, how-
>> Erik Hurst: Yeah, I have all of those slides. I'm trying to make sure I do that. But I'm just gonna give John a preview of some of the things that.

Cuz I wanna do a few more things and we could just take a look at some of the value function of the employed worker that's going to be in the background. I think we could talk about some of that after because all of that is going to be relatively standard in the points.

I'm not going to do that right now cuz I'm in the last 10 or 15 minutes, I do wanna show you a couple of results. But if anybody wants to take stay afterwards we could go through the value functions. We could go through.
>> John Cochrane: And then you solved it by some algorithm?

>> Erik Hurst: The solving is Andres and Andres solved it. And there's gonna be a large amount of state spaces with a bunch of bounds where this layoff margin is going to be. There's gonna be quits to unemployment thresholds. The inflation is going to move these kind of boundaries around.

So we're gonna have this kind of mapping of a set of decisions of firms and a set of decisions of workers that are going to be simultaneously having to be solved. That is a complicated problem beyond my skill set. But Andres and Andres have worked, as I say, they had to kind of get that but that is going to be around the background.

I would love to talk about that afterwards kind of the mechanics of the model because I do think there is some innovation in the modeling aspect to solve models with this kind of distribution that is going back on in the background. That is in addition to kind of some of the results that I wanna talk about.

>> John Cochrane: It wasn't easy, you make me feel better and not as dumb as I was.
>> Erik Hurst: No, it is quite complex. And again, I was trying to think of how to do an hour talk, that was what I cut in the our talk to try to give a flavor of the mechanisms.

But there is a lot of meat underneath in terms of the decision rules and firms in terms of the assets.
>> Harold Ulugh: There's no insurance against idiosyncratic risk, is that right? So when they-
>> Erik Hurst: Exactly, I mean, so there's no market on it. They know the distribution, so they have assets, they could get their consumption.

But when these things occur, your productivity drifts. There's no asset market on the background of that. And the shock that I'm gonna do in a second is gonna be an unexpected.
>> Harold Ulugh: Unemployment insurance, any of-
>> Erik Hurst: I don't have a government in the background. What I'm really gonna be looking at is we're in a steady state and then God changes the inflation in an MIT unexpected way.

And that's gonna be the kind of thing that's gonna trace up.
>> Speaker 13: You gonna show the distribution of W minus Z.
>> Erik Hurst: Yep, I'm gonna show you that, I'm gonna do one thing first, I'm gonna tell you how to calibrate the model quickly. And then I'm gonna show you kind of the patterns of the results and I'm gonna try to do a few more things before we conclude.

So I'm gonna just calibrate as already told you on all the labor market flows from workers of different types in the pre period. Match the wage distributions and the flows, probably not for time going to talk about it. But I am going to look at E flows by different parts of the distribution of wage distribution.

I'm gonna look at UD flows at different parts of the distribution. This is gonna be informative about some of the heterogeneity in the model and so the fact that high income people are gonna churn less. Our model is gonna infer that, if it's gonna be costly to post vacancies for these types of workers, and that's why they're churning less.

The fact that the U to E doesn't decline despite that it's because at the same time, on the UD. Workers at the bottom of the distribution are gonna have more of a preference for unemployment than people at the top. And so those two forces are gonna help pin down those fee parameters which are gonna give us churn in the model.

As John kind of forecasted early on, yeah.
>> John Cochrane: What inflation did you feed in for the simulation?
>> Erik Hurst: So let's now get to the parts. So everybody wants to get here, so let's get here now. So let's talk about what I'm gonna do with the model. So I'm gonna do two things, okay?

The first one is I'm going to assume at time zero we're in steady state, God comes down and gives us a 13% inflation rate. And I wanna trace out the dynamics of the model. That's not the real world, but it allows me to get the dynamics of the model from the one time shock just to kind of see how the dynamics of the model are separate from the dynamics of the inflation.

The second experiment I'm going to do is kind of another extreme where again, a one time temporary change in inflation. A one time change in the price level, and then everything goes back to in the bottle, a 2% inflation rate after that. Then the second thing I'm gonna do is I'm going to have the agents in the model get unexpected shocks to inflation that match the data in every period.

So I go on to a Tuesday and I say, the inflation rate was 3% this year and then I'm thinking it's gonna be back to 2% tomorrow. And then I get to tomorrow and then, it's 4% tomorrow and I'm gonna think it's going to be 2% the next day after.

So a series of unexpected MIT shocks, all of these temporary, are going through. So those are the two things, and that's gonna allow me to see to match the time series much better than I'm going to do with this one time shock. So the one time shock is going to allow us to learn about the dynamics and then the second one of the model.

And then the second one is gonna match more of the actual data that I'm gonna show you.
>> Speaker 13: The model's continuous time, though. So how did you do the shocks periodically?
>> Erik Hurst: You're basically kind of average over what looks like a month in the model, and that's where it's going to be.

And we're gonna try to do it exactly that way. So this is Joshua's question, I told you it was coming. So the green is going to be the distribution of those wage markdowns prior to the inflation shock. And you can see that is a bounded support job, Josh, for exactly the same reason, there's these endogenous flows.

If you basically wage ever gets too, too high relative to your productivity on the green side, firms are just going to fire you. You're too expensive. If the wage ever gets too low relative to your productivity, you're just going to quit. And so those are gonna be bounded distributions.

And again, from those figures that I skipped over, there's a set under which these decisions are made.
>> John Cochrane: This is the one time price level?
>> Erik Hurst: This is a one time price level shock.
>> John Cochrane: Do we wait some time to get back to steady state?
>> Erik Hurst: Yeah, I'm gonna show you all of those.

This is on impact. I'm sorry, the blue is right after impact. This is just Josh on impact. This is Josh's conjecture from early on. A 13% inflation rate is gonna move all of our wages down by 13%. But notice we move a lot from the layoff margin now.

And so this is gonna generate a big decline in layoffs in the model. So let me kind of show you now what's going to happen to the flows in response to this one-time shock. So on impact of this one time shock, you're going to get a whole bunch of churn occurring in the labor market.

People are gonna start looking for another job in response to the inflation, and that's going to eventually atrophy over time. So you're gonna get a lot of stuff occurring up front and then it's going to take time to get back down to a steady state. The vacancy to unemployment rate is going to jump with a little bit of a lag because on impact some of the low income people, when the real wage fell, quit to unemployment.

So you did get a spike in vacancies going up and a spike in unemployment. So there was a little bit of unit thing. That unemployment thing is very temporary, those workers get reabsorbed back and so you get a little shifted dynamic. But you get a shift in the vacancy to unemployment rate and then it kind of comes back down afterwards.

And you can see the churn that we're getting in this calibrated model. The E-E flow isn't that different than kind of what you see in the quit rate that we're observing in the data. So these magnitudes, even though it's a one-time shock, aren't that far out of line what you see in the data.

I don't want to take this too quantitatively because it is a different shock, but it is in the magnitudes that we are seeing in the data.
>> Speaker 13: Given the shift in the weight markdown distribution, there must be something in the model that's preventing the ED rate from going up a lot more.

Cuz there's a lot of people who just got hit with a big negative real weight shock that makes their weight markdown very large for them. Now, why aren't you getting in the model from this experiment? Bigger rise in EV.
>> Erik Hurst: So there's gonna be two different reasons I think some of which is Pete alluded to earlier.

Some people are gonna be moving back into their ranges. So then when they-
>> Speaker 13: Yeah, I understand.
>> Erik Hurst: And the second thing is you get some stuff for free. And then the third thing is some of us are gonna draw renegotiation costs that are relatively low that we don't have to churn to get the real wage increase.

And when I show you the real wage movements later on, not all of that is gonna come from the churn. Some of it's gonna come from a renegotiation on the job because we just go to your office and I get my office from Stanford. I come back.
>> Speaker 15: These are hard things to observe.

>> Erik Hurst: Yeah.
>> Speaker 15: And they're playing a big role in these adjustment dynamics, as I understand.
>> Erik Hurst: Exactly, so the thing is that disciplining it is the wage distribution in the pre period. Given that wage distribution in the pre-period.
>> Speaker 15: It's an indirect.
>> Erik Hurst: Exactly.
>> Speaker 15: Because we're not observing the opportunity to renegotiate in any direct way.

>> Erik Hurst: Exactly, but what you can see is the wage change of job stayers and how that evolves. And I'm gonna show you that in a few minutes. And we're gonna see how our model does on that relative to the data.
>> Speaker 15: Can I ask one more question? Don't vacancy durations go down-

>> Erik Hurst: In this one?
>> Speaker 15: In this experiment?
>> Erik Hurst: No, no, no, they go up in our experiment.
>> Speaker 15: Why is that?
>> Erik Hurst: Composition effect. Because now most, Steve say so the vacancy duration in the data has gone up. Okay, so we see, vacancy staying open longer using your method.

And then in our model we actually match that as well. But it's coming from the people when they're unemployed find a vacancy relatively quick. The E2E people find vacancy a little bit lower. They're just moving in normal times in their churn on the job ladder. So Steve's right, the EDE people actually find jobs quicker now.

But the shift from UDE churn to EDE turn is so large during this period that the composition effect moves the whole duration distribution up in this one because of composition. But Steve is right. For the EDE people, their duration is going down. Now I can't see that in the data, but I do see the composition shift from U2E to EDE was large in this period in terms of the searching.

And the ED people through the lens of the model just take longer to search than the UDE. So it's a complete composition fix during this time period. On impact, this is just in this large shock. As Josh said, layoff goes to zero immediately after everybody moves so far away from that with this big one time shock that everybody moves away from the layoff margin.

So you get a big decline in layoffs on impact, productivity effects or Pete's question going on. All of there's no match specific capital in the background. So we're not reallocating to better firms or not. I don't have that in the model. The UDE rate doesn't move in this model.

Again, some of that's hardwired in because I assumed that the unemployment margin was in real terms and so nothing was changing on that. And new hires are real, the unemployment margin is real. So nothing is changing on the UE ratio. Here's the wage changes for job changers and the wage changes for job stayers.

This is Steve's question on impact we're getting a large increase relative to steady state even for the job stayers. Why? Because they're gonna do the renegotiation with their firm. But the job changers in our model are getting exactly even more than that because by searching you're able to get to the flexible wages quicker.

These again magnitudes are roughly the same magnitudes that I showed you again. I don't want to take this part of the paper too quantitatively but I was comforted that they were at least in the same ballpark that we're observing of the magnitudes in the data. This is going to be the frequency of wage increases for jobsayers, this is Steve's question one more time is basically we're just renegotiation quicker during this period.

And again there's some evidence consistent of this. I don't have the ADP data yet the microdata like I used to. I am in process of trying to regain access to that cuz then I could actually measure this moment a lot quicker. But there is some in the Atlanta Fed data you are seeing the frequency of wage changes go up in that data as well for job stayers.

We get a big shift in the beverage curve just like we see in the data. Why? Cuz not much is moving on unemployment and we're getting a huge change in vacancies. So our model is generating a shift in the beverage curve during this time period. There's a little movement in the unemployment rate as people are moving into the unemployment pool, particularly on impact.

But those are small relative to the shift in vacancy. Here is the way job search and ED rates, I'm not gonna spend much time on this. I wanna show you one more thing before I conclude, is the distribution across the different types of job search and ED rates.

And in the model the load types, the blue are searching more and churning more because they were just more elastic in general. And so that's how they're gonna get more of the wage changes early on. And that's how we're gonna get the wage compression going on in the data.

And so I have some pictures on what happens to the wages of the different groups. This last picture I'm gonna show you on here and then I'm gonna show you one more thing before I conclude. But let me show you two slides and then we'll have a discussion after that.

So this is gonna be the welfare in one month's wage equivalent. So one is loss of one month's wages for different income groups run through the lens of our model. I group the Z's into deciles. And so there's 10 points on this, which is gonna be the average of the deciles.

And the bottom of the distribution is going to get less welfare losses than the top. But everybody's losing roughly a month of income on the background. And this is a chunk. I mean, I just want to make sure, so if the bottom of the distribution's earning, something I don't know, 25, 30,000, 40, that, whatever that is.

One month of that is enough to get people up in arms where they would be hating inflation. And the top of the distribution is gonna be about one month of income there as well. And the level of income is gonna be higher. So the level of dollars.
>> Harold Ulugh: The data showed us that real wages went down by 4%.

>> Erik Hurst: So now the Harold's part. Let's break it into its components now. So the sum of the four colors are going to then add up to those line that I just showed you. The blue in this is Harold's part, which is how much of that is just due to the real wage decline in general.

And to a first approximation, it's a chunk of it. I mean, so most of this is the real wage decline on average.
>> Harold Ulugh: In fact, if you just focus on that, you would get the same number.
>> Erik Hurst: You'd get roughly the same number. Exactly, because the purples and the orange and the greens cancel out.

Now, the purple is way too large. And I'll tell you why the purple is way too large in a second in this experiment. We're in the process of doing this now for this series of MIT shocks coming through. But let me just kind of go through. The yellow or the orange is gonna be the renegotiation costs.

The green, which you can barely see with your eyes, is going to be the search cost because there's a lot of churn in the labor market as well. The additional churn that's coming through is there. It is just relatively small the way we parameterize this compared to the renegotiation costs.

Now, I should make a comment that some of the renegotiation costs could actually be search costs. I go out and try to get an offer from Stanford to come back and renegotiate with the Booth Deans. That is a search behavior that will actually look like in the data for the reason Steve said renegotiation.

So in the way I kind of write it up in the paper, I kind of clump the orange and the green together for the reason you said. I can't really separate the two. All I could really see is the net effect of the costly actions. The purple is the gains you get from moving so far away from the layoff margin.

Now, this shock was so big that everybody moved away from the layoff margin. That is very large in the way I parameterize the shock when I do the series of MIT shocks, that purple thing is much smaller because here the big shock just took everybody away. Layoffs went to zero in the economy.

And so that is kind of a big thing. That is the one thing we're working on recalibrating this picture for what I'm gonna show you next, the series of MIT shocks. Yeah, John.
>> John Cochrane: I can see that a model would tell us about marginal search and renegotiation costs, but I think you could add kind of arbitrary fixed cost to that.

Which is always the problem of welfare things is that they don't really pin that down really well.
>> Erik Hurst: Yeah, so-
>> John Cochrane: It's the discrete choices here that reveal something about the fixed cost in the model.
>> Erik Hurst: The way we've parameterized the levels and the elasticities are kind of related.

Yeah, and so that is. Yeah, I'm open for thoughts on how we can kind of move around from some of that. But John is right. So we're using the flows in the pre-period that gives us both the levels and the elasticities. And that is gonna be important when we do these welfare concepts.

>> John Cochrane: You have some discrete choices like do I search at all?
>> Erik Hurst: Yep.
>> John Cochrane: That measures fixed costs.
>> Erik Hurst: Yeah, we get that in the pre period. So we got some of this and so we got some of that in the pre period. Now the question is, I do think there's other moments I could be potentially doing to try to pin these elasticities down a little bit more, which I haven't done, yeah.

>> John Cochrane: I speak of someone who finds search and renegotiation big pain in the butt. Yes, pain in the butt costs.
>> Erik Hurst: Yes, that's exactly. But Harold's point is, at least in this parameter, it's really the real wage losses that is driving a lot of this action. Now the green and the yellow is about 20% of the wage loss there offset by about a 20% of the welfare gain you're getting from the decline in the layoff margin.

But 20% isn't nothing. But it is the real wage losses is the predominant.
>> Harold Ulugh: Source of this picture, I think also sheds light on a completely different theme. In Europe there's more job security, all kinds of rules. They probably come at the cost of lower wages, right? I mean the job security gives you the perfect stuff, but they get the lower wage.

We could probably do multiple comparisons.
>> Erik Hurst: That would be a different context, exactly. Use the same kind of framework to go to that kind of question. I think that would be very interesting. Let me kind of show you now I'm gonna feed in just to get a rough sense of the magnitudes that are kind of coming along.

I'm now going to just feed in the actual inflation series, and every time it comes along it's like an unexpected MIT shock. Again, the expectations of this is really weird. The truth is, somewhere probably in between, if they knew the whole path at time T, it would probably look somewhat like the one time shock, but not completely.

There would be some smoothing out in this. This is basically every moment is unexpected coming through.
>> Speaker 14: So that's known as a Simsa sequence of shocks. That's how they-
>> Erik Hurst: Okay.
>> Speaker 14: That's how they calculated their counterfactuals, is they were repeatedly fooling everybody.
>> Erik Hurst: Exactly, this is exactly what this is.

This is the other extreme that we've done so far.
>> Speaker 14: Sims Za.
>> Erik Hurst: Okay, so I thought you said Sim Shaw. And I thought it was like a phrase or something, but it was Sims.
>> John Cochrane: And a forecast throughout this period are perfectly modeled as an AR1, back to 2%.

>> Erik Hurst: Yeah.
>> John Cochrane: So you could-
>> Erik Hurst: We could feed that in. And so that's another thing that we could do. So we're working on that, on how we could try to get some of that expectation through kind of the boundary conditions in the middle. But that is something we're working on now.

I told you there was one or two, I told John. It's evolving because that's the next shock we want to do is just put in the Fed's forecast at time zero and kind of go through with that.
>> John Cochrane: Forecast at each state if you want.
>> Erik Hurst: Well, you could do that.

But I was just thinking, even the one, the Fed score get it, yeah. That kind of gives you the upper bound on that. But the key thing is we match the time patterns and the magnitudes a little bit better in terms of the data from these kind of series of repeated shocks as opposed to the one time shock.

And then you can see that in ED flows, we're basically matching the data pretty closely. We went for something like 2.2 to 2.5 in kind of the ED flows that we're seeing. The data here, we're going from 2.2, 2.1 to 2.4. So it's in the same kind of ballpark that we're seeing.

>> Harold Ulugh: Nice to see the data line here.
>> Erik Hurst: Yeah, no, I thought of it, I thought of that this morning when I showed overlay the data on part of it. We're still getting a lot of action on the layoff margin even in this model. So the second thing we're doing is smoothing out the layoff margin in the data because here we're still getting a 50% decline in layoffs and the data's got about 20%.

So we're still over predicting on that. So we're thinking of how to match that moment a little bit more. Okay, let me kind of just kind of show two things. And this is the kind of thing I like. So now I'm gonna say, does my model hold any water in other ways.

So how do we go back in time? And so this is the vacancy to unemployment rate for US data going back to 1950. There are I think nine periods there where the spike in the or eight periods where the spike in the vacancy to unemployment rate was relatively large compared to the mean.

I put triangles on four of them and circles on four of them. What are those going to be? Well, the circles. Yeah, I wanna do the triangles first. So let's do the triangles first. I flipped the order of this when I did slide last night. Those are periods that look like traditional hot labor market standard beverage curve stories.

What do I mean by that? These are periods when the inflation rate was pretty low. The inflation rate, I mean the unemployment rate was low and it was declining as the vacancy to unemployment rate was going up. It looks like you're moving along kind of a beverage curve.

So all of these periods had 2 to 4% inflation rates. Unemployment rate in the 4 to 5%. And in the pre period to the spike the unemployment rate was going down usually from some number like 6 or 7% during this period. It looks like you're moving along a traditional beverage curve.

There are four other periods when we would say that the labor market didn't look over. Really hot during that time period. So these are gonna be 1951, 1973, 1979, or right the before 73, 78. There the unemployment rate was 5 to 7%. And it wasn't declining in the periods prior to the spike in the unemployment, in the vacancy to unemployment rate.

But here the inflation rate was relatively high and rising during this time period. So you're seeing 1974, 1979 were periods of high vacancy to unemployment rate. But nobody would really say that was kind of a hot labor market during that period, at least by unemployment dynamics. So what if I just projected the vacancy to unemployment rate on the unemployment rate, kind of trace out the beverage curve, take the inflation rate projected on the unemployment rate, take the residuals of that and just correlate the residuals together.

You could see that in periods of high inflation relative to the unemployment rate were also periods of high vacancy to unemployment rate relative to the unemployment rate. So it seems something about the nature of the vacancy to unemployment rate seems to positively be covarying with the inflation in the economy.

And I have regressions in the paper. And then instead of doing the vacancy to unemployment rate, I just show you the vacancy rate as well. You get very similar patterns, so vacancies seem to be going up. Eventually I wanna get E to E flows, so I'll talk to Steve later, can I get E to E flows going back to 1950 or 1951?

But again, really, cuz our mechanism is that you're gonna get a movement towards E to E flows away from U to E flows. That churn in the labor market is what's causing the vacancy to unemployment rate to go up in periods of high inflation. And so it does seem like there's some what you know, this theory is holding a little bit of water in periods, at least on the surface, outside the current, the current inflationary episode.

So we end the paper by just feeding in a lot of other shocks into our model and see how well they do along a variety of dimensions. Even though it's complex, it's parsimonious, there's only a couple other things I could shock through the lens of our model. So I could shock productivity in the economy.

I could shock what I'm gonna call labor demand. These are gonna be things that are gonna be able to move around firm hiring decisions. So the cost of job vacancy posting, maybe the discount rate in the model, getting firms to potentially hire a little bit earlier. And I could shock around the taste for leisure.

Through the lens of the model, I'm gonna calibrate those shocks so they all match the same vacancy to unemployment rate ex ante. So I'm gonna get the shocks to match the rise in the vacancy unemployment rate according to our baseline model. So all of them match the vacancy to unemployment rate by the same magnitude by design.

What happens to all of the other mechanisms in the model? And you can see it is hard for these other shocks to get the relatively large increase in E to E flows relative to U to E flows. It is hard for them to get real wages falling, cuz most of these shocks are positive labor market shocks to raise the vacancy to unemployment rate.

Which usually mean wages go up, either labor demand goes up or our labor supply goes down, both of which put upward pressure on real wages. So those are gonna struggle to match the real wage declines. You can see that the wage growth of switchers relative to stayers is always higher, cuz that's what we calibrate the switchers.

But the change during this period is much higher in our model in terms of the wage growth of the switchers relative to stayers in any of these other models. So these other models kinda struggle with what called pure labor market shocks to kinda match jointly the flows where our model is pretty successful on that dimension.

And so this is my last slide, which begs the question, what caused inflation to go up during this period and how would that potentially interact with the labor market? Well, the literature kind of has two types of stories that are going on. A negative supply shock, it may be a positive demand shock.

A negative supply shock puts downward pressure on the vacancy to unemployment rate, puts downward pressure on real wages, puts downward pressure on the U to E rate, causes employment to fall. A positive, we'll call labor demand shock, something like government spending or things of those natures does the opposite.

And if those both things happened at the same time, it's possible that those things, the true effects of those things on the labor market roughly offset. And you might be left with the inflation things. The point with this part is these other shocks that people are telling have offsetting effects on the labor market.

And so you need a different type of exercise to try to infer what the causes of the inflation were through the lens of our model. But it's possible that if these things had roughly offsetting forces, our inflation shock could be a driver that is explaining a lot of the inflation, the labor market dynamics during this period.

Let me go Josh first and then-
>> Josh Raul: What about work from home shock that happened at the same time all of a sudden if your commuting costs go to zero, then that might explain. You said that-.
>> Erik Hurst: Take one thing more with that. So suppose it's an amenity now.

So basically you're going to. Commuting costs go down in some sectors and I wanna move to those sectors potentially because I like working from home and you don't. So that's gonna generate some churn. But in that model, the wage growth of the job switchers would actually be lower than it would be because I'm gonna compensate some of the amenities.

So for that one, the wage growth of the switchers is going to hard to generate in those models of work from home as being a primary shock. That could do good on other margins. It could get the average wages going down, it could get some churn. But getting the wage growth of the switchers versus stayers those models would potentially struggle with.

>> John Taylor: That's under assumption flexibility wages for switcher but not for stayers.
>> Erik Hurst: Yeah, under the lens of the model I wrote down. And then we might say that you might not want that model written down, but if you wanted to have that model, that would be. Bob.
>> Robert Hall: I'm somewhat of a student of this topic.

Implicit comparison here between a relatively straightforward New Keynesian model, that's kind of the starting point. And then and then a critique of that model because it doesn't fit a lot of the things that you've brought in data which we don't normally New Keynesian model. So then you could say, here's what the New Keynesian model gets wrong, which is fixed by this-.

>> Erik Hurst: I don't have a lot of other features. I took some one element of the New Keynesian model, sticky wages, and put it in a standard search model. So it's a search model with New Keynesian. If I wanted to have that critique of the New Keynesian model, I think I'm going to need a few more bells and whistles that I don't have.

But I do think there are things that those New Keynesian models would have predictions about, like the wage changes of switchers versus stayers that they might fail to match in some of their models. But I have not written that model. So I've started with a search model with one New Keynesian feature, as opposed to a New Keynesian model and then putting in a couple of search features, so-.

>> Robert Hall: Okay, so then you could start, that's a legitimate starting point.
>> Erik Hurst: That's what I thought where I was starting. And so given that through the lens of my model, these other shocks would struggle to match some of the patterns that I've showed you. Thank you, I'm out