Appreciate the insights (and the forecast/assessment regarding restrictiveness of monetary policy).

Regarding the u/v measure - I've been wondering about two things:

1. Regarding v - there is some anecdotal evidence of 'fake' job postings to look stronger than the company actually is;

2. Regarding u - there is about 4.5 mln out of labor force folk who say they'd want a job. Now I haven't investigated the historical trend (i.e. maybe this is a standard number) but if there is now a shift of people going for out of labor force directly to employment, what would the complication be for measuring tightness? Of course it would mean there is more slack - but I'm wondering of how big this channel could theoretically be (i.e. is unemployment under counted by 100k or by 1mln)

On the fake vacancies: I’m just not sure what this means. Is this supposed to be a new phenomenon? If so, when and why did it start? Firms have been posted vacancies for a century at least, so why would vacancies become fake now? If it’s not new, it implies that vacancy data are meaningless. But going back to 1930, we find that vacancy data are very meaningful. They co-move with unemployment, describing a clearly visible Beveridge curve. The Beveridge curve is one of the most robust macro relationships—how would it arise if vacancy data were fake? (See for instance figure 12 in https://pascalmichaillat.org/13.pdf.)

On the unemployment rate: it’s true that there are some people outside of the labor force who would like to work. They are counted in the U4 and U5 measures of unemployment, but not in the standard U3 measure that is reported above. The number of people who are not counted as unemployed but who want a job is U5-U3. This number is stable over time: roughly always 1% of the labor force. (See for instance slide 8 in https://pascalmichaillat.org/13p.pdf.)

Because the marginal unemployment rate is roughly constant over time, it does not affect our efficiency calculations. The efficient tightness remains 1 whether or not these workers are taken into account. The efficient unemployment rate can be expressed in two equivalent ways: U3* = 4.4%, as in this post, or U5* = U3* + 1% = 5.4%. This extra 1% of workers corresponds to 1.6 million workers with today's labor force.

Regarding the vacancies - it was mainly a reference to what has been recently discussed in certain media outlets. So it would be a recent phenomenon rather than a historic one. One reason mentioned here - https://www.cbsnews.com/news/job-openings-fake-listings-ads-federal-reserve-jolts/ - there could be certain double posting occuring due to virtual and non-virtual job. This could be a tactic to have a wider job posting audience. This would be unique to current times. Another suggestion (but this may have occurred in the past too) is that with higher quit rates, you may need more job postings at any given time to go through churn.

Thank you for sharing this article! It's very interesting. The main point is contained in this paragraph: "When you have fewer candidates per opening, you have to be more creative, create more job titles for positions. The high openings figure does partly reflect recruiting intensity, and not actual roles and seats and slots." From this the journalist infers that vacancies are not a meaningful statistic. But in our models, this is exactly what vacancies are supposed to be! They do no represent actual position but recruiting intensity. In the model, if a firm wants to recruit one worker this month but knows that a vacancy is only filled with probability 1/3, then the firm will post 3 vacancies to hire one worker in expectation (see for instance the derivation on p. 6 at https://pascalmichaillat.org/14.pdf).

So the bottom line is firms behave exactly as in the model. Since it is hard to find workers, and a lot of workers quit, firms have to post many vacancies to replenish their ranks. And of course they will post vacancies in different locations, for different positions, and with different modalities (online or in-person) to increase the chances of matching with a suitable worker. Posting the exact same vacancy many times would not be effective.

The labor market is currently exceptionally tight: the tightest it has been since the end of World War 2. This means that vacancies are filled at the slowest rate in the postwar period. At a result, the multiplication of vacancies posted for one actual position has exploded. But this is not an issue: it is exactly what the model predicts. If firms did not do that, our model would be useless.

Thank you again for pointing to this article. I had not fully understood what people meant when they talked about fake vacancies. I may need to write a full-length post about this!

Regarding the need for unemployment to rise, I think there’s good reasons no to think so, both having to do with non-linearities. One in the Phillips Curve in the just release Benigno-Eggertson paper (where you probably consulted), the other in the Beveridge curve, discussed in this great Twitter thread by Simon Mongey. This thread also challenges the notion of a shifting out of the BC recently.

Hi Filippos! I am not sure I agree, but I am grateful for the comment!

I do know the Benigno-Eggertsson paper well—indeed I've talked to Gauti a fair amount about it. One of the motivations for it was our "u*=√uv" paper, on which this post is based. In the paper we note that there are only 4 periods in US recorded history when the labor market is inefficiently tight (that is, tightness>1): World War 2, Korean War, Vietnam War, and the post-pandemic recovery. Gauti saw this and realized, brilliantly, that these 4 periods were also periods of high inflation. So he started building a model of a nonlinear Phillips curve with a kink where tightness = 1. What the model says is that the Phillips curve is steep when tightness is above 1, like today. However, to bring inflation back to target, it is still necessary to bring tightness back to 1. And this requires a movement along the Beveridge curve, which will lead to higher unemployment. The only way this will not happen is if the Beveridge curve shifts back inward.

What our "u*=√uv" paper shows is that the Fed should bring tightness to 1 to meet its full-employment mandate. What the Benigno-Eggertsson paper adds is that the Fed will also meet its price-stability mandate by bringing tightness to 1! So the divine coincidence might actually hold in the data, at a tightness of 1.

I am not sure I understand the Mongey point that the Beveridge curve has not shifted out. The Beveridge curve is the locus of points in the unemployment-vacancy space. This is the graph above in the post. Obviously the Beveridge curve has shifted out. In fact, the outward shift following the pandemic is the largest shift in the Beveridge curve since the one that happened right after the Great Depression. I've added a graph in the above post to illustrate both these Beveridge shifts.

A basic manifestation of the fact that the Beveridge curve has shifted out is that the unemployment rate is at the same level as before the pandemic level (3.5% in Feb. 2020), but the vacancy rate and tightness are much, much higher (tightness is now 1.7 instead of 1.2 in Feb. 2020). So we cannot be on the same curve. Am I missing something ?

I think Mongey’s point is that we are (probably were, until a few months ago) at a point where the Beveridge Curve becomes almost vertical. At very high V and given decreasing returns, what shows up as a shift out of the BC is just an increase in V with flat U along the same BC, due to these second round effects. See this photo (lhs).

To be fair, of course there was a shift out in the first couple of months of the pandemic, but I think his point is that we quickly returned to the previous BC, but at a steeper point.

Gauti also gives higher odds of a soft landing, again due to the steepness of the PC - fall in V without much change in U.

- The empirical Beveridge curve is not vertical, even at very high tightness. Empirically, the Beveridge curve has a constant elasticity, even at very high tightness. You can see that the Beveridge curve is isoelastic over the 1951–2019 period in figure 5 at https://pascalmichaillat.org/9.pdf. And the graph at the bottom of this post shows that the Beveridge curve was also isoleastic during the 1930–1950 period, which saw tightness reach 7! Furthermore, the elasticity is always close to 1. So when the number of vacancies falls by 1%, the number of unemployed workers always increases by 1%.

- Gauti's argument is incorrect. Notice that he mixes the Phillips curve, which is a relation between inflation and output and appears in the first tweet, and the Beveridge curve, which is a relation between vacancies and unemployment and appears in the second tweet. The slope of one has nothing to do with the slope of the other. In fact in his model, the labor market is always on the Beveridge curve, so when vacancies drop, unemployment must rise. The vertical drop of the Beveridge curve that he shows, the same as in this post, is not consistent with his model or any matching model. His model, and any matching model, predicts that unemployment should have increased in the past few months as vacancies were falling "like a rock". Through the lens of the matching model, what we see now is akin to an inward shift of the Beveridge curve. It is not something that the models can predict.

- Also note that Mongey's tweets do not plot the standard Beveridge curve: there is no large increase in unemployment after the pandemic. It seems that he adjusts the pool of unemployed in various ways to reflect search intensity, for instance by excluding workers on temporary layoffs. So the predictions do not speak to the total number of unemployed workers: the analysis is looking at something else.

- Also note that the second-round effects only occur because Mongey is using a linearized version of the Beveridge curve, based on a specific structural model. In the analysis above I take the nonlinear (in fact isoelastic) Beveridge curve as given, based on its empirical properties, without trying to impose a structure to it (in the spirit of the sufficient-statistic approach). I am not assuming it is linear in any way.

I hope this makes sense. Thanks again for the questions, comments, and links!

Indeed, it will be very interesting to see what happens to the Beveridge curve, and inflation.

I've also thought more about the Beveridge curve in Gauti's model, and talked to him about it. I do think that you cannot have a drop in vacancies without an increase in unemployment in the model.

Take equation (8), which is their Beveridge curve (p. 20 at https://www.nber.org/system/files/working_papers/w31197/w31197.pdf). Divide both sides by participation F. You get n(t) = 1 - s + s f(theta(t)), where n(t) is the employment rate. Next, n(t) = 1 - u(t), where u(t) is the unemployment rate, and theta(t) = v(t) / u(t), where v(t) is the vacancy rate. So equation (8) becomes 1 - u(t) = 1 - s + s f(v(t) / u(t)), or:

u(t) = s - s f(v(t) / u(t)).

If v(t) falls, u(t) cannot remain the same—otherwise equation (8) is violated. In fact, u(t) has to increase since the job-finding rate f is increasing. A drop in vacancy is necessarily followed by an increase in unemployment. The Beveridge curve always holds.

Notice also that equation (8) holds irrespective of where the economy is on the Phillips curve. So it’s not the case that the relationship between unemployment and vacancies is different than in the past. The response of inflation to a change in tightness might be different now, but not the response of unemployment to a change in tightness.

For what its worth, if you used only the constant elasticity that you advocated then you'd have had negative unemployment. Whether you understood this or not it wrongly meant that your view implied that you could only reconcile the data with a shift. This was the same mistake that Blanchard, Domash and Summers made in their piece. Any way we cut measures of match efficiency there was no argument to be made that there was a shift in converting vacancies and searchers into hires that persisted much beyond late-2021.

Hi Simon! Thank you very much for the comments and for sharing the update. I find the update extremely interesting—I was surprised by the vacancy trend that you isolate, and the shape of the detrended Beveridge curve. I would love to talk about this with you. There are still a few things that I have not been able to understand. I will send you an email.

In the meantime, here are a few disjointed comments:

- The Beveridge curve that we use is an hyperbola, u = A/v, so it never leads to negative unemployment or vacancy. Irrespective of the location A, u>0 and v>0.

- Not sure if that matters, but Blanchard, Domash, and Summers have an error in their derivation of the Beveridge curve. They assume that the number of hires is exogenous, while typically the number of hires is equal to the number of separations, which itself depends on the unemployment rate: separations = s x (1-u), where s is the separation rate. So they do not use the canonical expression for the Beveridge curve (what you would find in Pissarides's textbook). Their calibration also implies a Beveridge curve that is too flat.

- In the update you note that the current tightness is unprecedented. While that is true in the postwar period, tightness was actually much higher than today just after World War 2 (v/u reached 7 then, see figure 10 in https://pascalmichaillat.org/13.pdf). And the Beveridge curve was not vertical then, it had an elasticity of 0.8 (see figure 9 in https://pascalmichaillat.org/13.pdf). Of course the data are quite noisy.

Appreciate the insights (and the forecast/assessment regarding restrictiveness of monetary policy).

Regarding the u/v measure - I've been wondering about two things:

1. Regarding v - there is some anecdotal evidence of 'fake' job postings to look stronger than the company actually is;

2. Regarding u - there is about 4.5 mln out of labor force folk who say they'd want a job. Now I haven't investigated the historical trend (i.e. maybe this is a standard number) but if there is now a shift of people going for out of labor force directly to employment, what would the complication be for measuring tightness? Of course it would mean there is more slack - but I'm wondering of how big this channel could theoretically be (i.e. is unemployment under counted by 100k or by 1mln)

edited May 5, 2023These are great questions.

On the fake vacancies: I’m just not sure what this means. Is this supposed to be a new phenomenon? If so, when and why did it start? Firms have been posted vacancies for a century at least, so why would vacancies become fake now? If it’s not new, it implies that vacancy data are meaningless. But going back to 1930, we find that vacancy data are very meaningful. They co-move with unemployment, describing a clearly visible Beveridge curve. The Beveridge curve is one of the most robust macro relationships—how would it arise if vacancy data were fake? (See for instance figure 12 in https://pascalmichaillat.org/13.pdf.)

On the unemployment rate: it’s true that there are some people outside of the labor force who would like to work. They are counted in the U4 and U5 measures of unemployment, but not in the standard U3 measure that is reported above. The number of people who are not counted as unemployed but who want a job is U5-U3. This number is stable over time: roughly always 1% of the labor force. (See for instance slide 8 in https://pascalmichaillat.org/13p.pdf.)

Because the marginal unemployment rate is roughly constant over time, it does not affect our efficiency calculations. The efficient tightness remains 1 whether or not these workers are taken into account. The efficient unemployment rate can be expressed in two equivalent ways: U3* = 4.4%, as in this post, or U5* = U3* + 1% = 5.4%. This extra 1% of workers corresponds to 1.6 million workers with today's labor force.

Regarding the vacancies - it was mainly a reference to what has been recently discussed in certain media outlets. So it would be a recent phenomenon rather than a historic one. One reason mentioned here - https://www.cbsnews.com/news/job-openings-fake-listings-ads-federal-reserve-jolts/ - there could be certain double posting occuring due to virtual and non-virtual job. This could be a tactic to have a wider job posting audience. This would be unique to current times. Another suggestion (but this may have occurred in the past too) is that with higher quit rates, you may need more job postings at any given time to go through churn.

Thank you for sharing this article! It's very interesting. The main point is contained in this paragraph: "When you have fewer candidates per opening, you have to be more creative, create more job titles for positions. The high openings figure does partly reflect recruiting intensity, and not actual roles and seats and slots." From this the journalist infers that vacancies are not a meaningful statistic. But in our models, this is exactly what vacancies are supposed to be! They do no represent actual position but recruiting intensity. In the model, if a firm wants to recruit one worker this month but knows that a vacancy is only filled with probability 1/3, then the firm will post 3 vacancies to hire one worker in expectation (see for instance the derivation on p. 6 at https://pascalmichaillat.org/14.pdf).

So the bottom line is firms behave exactly as in the model. Since it is hard to find workers, and a lot of workers quit, firms have to post many vacancies to replenish their ranks. And of course they will post vacancies in different locations, for different positions, and with different modalities (online or in-person) to increase the chances of matching with a suitable worker. Posting the exact same vacancy many times would not be effective.

The labor market is currently exceptionally tight: the tightest it has been since the end of World War 2. This means that vacancies are filled at the slowest rate in the postwar period. At a result, the multiplication of vacancies posted for one actual position has exploded. But this is not an issue: it is exactly what the model predicts. If firms did not do that, our model would be useless.

Thank you again for pointing to this article. I had not fully understood what people meant when they talked about fake vacancies. I may need to write a full-length post about this!

Hi Pascal,

Regarding the need for unemployment to rise, I think there’s good reasons no to think so, both having to do with non-linearities. One in the Phillips Curve in the just release Benigno-Eggertson paper (where you probably consulted), the other in the Beveridge curve, discussed in this great Twitter thread by Simon Mongey. This thread also challenges the notion of a shifting out of the BC recently.

https://twitter.com/simon_mongey/status/1590705225161408512?s=21&t=aMBhh3gK7weGIUdfICGsLQ

edited May 6, 2023Hi Filippos! I am not sure I agree, but I am grateful for the comment!

I do know the Benigno-Eggertsson paper well—indeed I've talked to Gauti a fair amount about it. One of the motivations for it was our "u*=√uv" paper, on which this post is based. In the paper we note that there are only 4 periods in US recorded history when the labor market is inefficiently tight (that is, tightness>1): World War 2, Korean War, Vietnam War, and the post-pandemic recovery. Gauti saw this and realized, brilliantly, that these 4 periods were also periods of high inflation. So he started building a model of a nonlinear Phillips curve with a kink where tightness = 1. What the model says is that the Phillips curve is steep when tightness is above 1, like today. However, to bring inflation back to target, it is still necessary to bring tightness back to 1. And this requires a movement along the Beveridge curve, which will lead to higher unemployment. The only way this will not happen is if the Beveridge curve shifts back inward.

What our "u*=√uv" paper shows is that the Fed should bring tightness to 1 to meet its full-employment mandate. What the Benigno-Eggertsson paper adds is that the Fed will also meet its price-stability mandate by bringing tightness to 1! So the divine coincidence might actually hold in the data, at a tightness of 1.

I am not sure I understand the Mongey point that the Beveridge curve has not shifted out. The Beveridge curve is the locus of points in the unemployment-vacancy space. This is the graph above in the post. Obviously the Beveridge curve has shifted out. In fact, the outward shift following the pandemic is the largest shift in the Beveridge curve since the one that happened right after the Great Depression. I've added a graph in the above post to illustrate both these Beveridge shifts.

A basic manifestation of the fact that the Beveridge curve has shifted out is that the unemployment rate is at the same level as before the pandemic level (3.5% in Feb. 2020), but the vacancy rate and tightness are much, much higher (tightness is now 1.7 instead of 1.2 in Feb. 2020). So we cannot be on the same curve. Am I missing something ?

I think Mongey’s point is that we are (probably were, until a few months ago) at a point where the Beveridge Curve becomes almost vertical. At very high V and given decreasing returns, what shows up as a shift out of the BC is just an increase in V with flat U along the same BC, due to these second round effects. See this photo (lhs).

https://twitter.com/Simon_Mongey/status/1590705261672824833/photo/1

To be fair, of course there was a shift out in the first couple of months of the pandemic, but I think his point is that we quickly returned to the previous BC, but at a steeper point.

Gauti also gives higher odds of a soft landing, again due to the steepness of the PC - fall in V without much change in U.

https://twitter.com/gautieggertsson/status/1654646004401020929?s=46&t=jm9XIa90QMG7ICPs9R5sNA

edited May 8, 2023Thank you, Filippos. A couple of points:

- The empirical Beveridge curve is not vertical, even at very high tightness. Empirically, the Beveridge curve has a constant elasticity, even at very high tightness. You can see that the Beveridge curve is isoelastic over the 1951–2019 period in figure 5 at https://pascalmichaillat.org/9.pdf. And the graph at the bottom of this post shows that the Beveridge curve was also isoleastic during the 1930–1950 period, which saw tightness reach 7! Furthermore, the elasticity is always close to 1. So when the number of vacancies falls by 1%, the number of unemployed workers always increases by 1%.

- Gauti's argument is incorrect. Notice that he mixes the Phillips curve, which is a relation between inflation and output and appears in the first tweet, and the Beveridge curve, which is a relation between vacancies and unemployment and appears in the second tweet. The slope of one has nothing to do with the slope of the other. In fact in his model, the labor market is always on the Beveridge curve, so when vacancies drop, unemployment must rise. The vertical drop of the Beveridge curve that he shows, the same as in this post, is not consistent with his model or any matching model. His model, and any matching model, predicts that unemployment should have increased in the past few months as vacancies were falling "like a rock". Through the lens of the matching model, what we see now is akin to an inward shift of the Beveridge curve. It is not something that the models can predict.

- Also note that Mongey's tweets do not plot the standard Beveridge curve: there is no large increase in unemployment after the pandemic. It seems that he adjusts the pool of unemployed in various ways to reflect search intensity, for instance by excluding workers on temporary layoffs. So the predictions do not speak to the total number of unemployed workers: the analysis is looking at something else.

- Also note that the second-round effects only occur because Mongey is using a linearized version of the Beveridge curve, based on a specific structural model. In the analysis above I take the nonlinear (in fact isoelastic) Beveridge curve as given, based on its empirical properties, without trying to impose a structure to it (in the spirit of the sufficient-statistic approach). I am not assuming it is linear in any way.

I hope this makes sense. Thanks again for the questions, comments, and links!

All good points, will be interesting to see how this plays out over the next few months.

Indeed, it will be very interesting to see what happens to the Beveridge curve, and inflation.

I've also thought more about the Beveridge curve in Gauti's model, and talked to him about it. I do think that you cannot have a drop in vacancies without an increase in unemployment in the model.

Take equation (8), which is their Beveridge curve (p. 20 at https://www.nber.org/system/files/working_papers/w31197/w31197.pdf). Divide both sides by participation F. You get n(t) = 1 - s + s f(theta(t)), where n(t) is the employment rate. Next, n(t) = 1 - u(t), where u(t) is the unemployment rate, and theta(t) = v(t) / u(t), where v(t) is the vacancy rate. So equation (8) becomes 1 - u(t) = 1 - s + s f(v(t) / u(t)), or:

u(t) = s - s f(v(t) / u(t)).

If v(t) falls, u(t) cannot remain the same—otherwise equation (8) is violated. In fact, u(t) has to increase since the job-finding rate f is increasing. A drop in vacancy is necessarily followed by an increase in unemployment. The Beveridge curve always holds.

Notice also that equation (8) holds irrespective of where the economy is on the Phillips curve. So it’s not the case that the relationship between unemployment and vacancies is different than in the past. The response of inflation to a change in tightness might be different now, but not the response of unemployment to a change in tightness.

My whole point was *not* to linearize, and note that the second order terms were consistent with (a) the position of the U.S. economy, (b) no shift. It was immaterial whether we excluded workers on temporary layoff or not. The data since then has been completely consistent with that view. You might find this update interesting: https://www.minneapolisfed.org/article/2023/are-job-vacancies-still-as-plentiful-as-they-appear-implications-for-the-soft-landing

For what its worth, if you used only the constant elasticity that you advocated then you'd have had negative unemployment. Whether you understood this or not it wrongly meant that your view implied that you could only reconcile the data with a shift. This was the same mistake that Blanchard, Domash and Summers made in their piece. Any way we cut measures of match efficiency there was no argument to be made that there was a shift in converting vacancies and searchers into hires that persisted much beyond late-2021.

Happy to discuss more some time!

Hi Simon! Thank you very much for the comments and for sharing the update. I find the update extremely interesting—I was surprised by the vacancy trend that you isolate, and the shape of the detrended Beveridge curve. I would love to talk about this with you. There are still a few things that I have not been able to understand. I will send you an email.

In the meantime, here are a few disjointed comments:

- The Beveridge curve that we use is an hyperbola, u = A/v, so it never leads to negative unemployment or vacancy. Irrespective of the location A, u>0 and v>0.

- Not sure if that matters, but Blanchard, Domash, and Summers have an error in their derivation of the Beveridge curve. They assume that the number of hires is exogenous, while typically the number of hires is equal to the number of separations, which itself depends on the unemployment rate: separations = s x (1-u), where s is the separation rate. So they do not use the canonical expression for the Beveridge curve (what you would find in Pissarides's textbook). Their calibration also implies a Beveridge curve that is too flat.

- In the update you note that the current tightness is unprecedented. While that is true in the postwar period, tightness was actually much higher than today just after World War 2 (v/u reached 7 then, see figure 10 in https://pascalmichaillat.org/13.pdf). And the Beveridge curve was not vertical then, it had an elasticity of 0.8 (see figure 9 in https://pascalmichaillat.org/13.pdf). Of course the data are quite noisy.

I look forward to talking more!