Pascal Michaillat @pmichaillat Twitter profile

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Pascal Michaillat

@pmichaillat

29 days

Our attempt at modeling p-hacking and correcting for it.

The Review of Economics and Statistics (REStat)

@restatjournal

29 days

Just Accepted new paper, “Critical Values Robust to P-hacking” by Adam McCloskey and Pascal Michaillat

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Pascal Michaillat

@pmichaillat

21 days

Need a bit of technical support to get through first-year PhD math camp? The page hosts three short, basic notes covering mathematical methods for graduate macroeconomics: 1. Dynamic programming 2. Optimal control 3. Differential equations

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Pascal Michaillat

@pmichaillat

4 months

Looking for a LaTeX template for your research papers? The 2024 version of the template offers: - new font of math symbols - new blackboard-bold font - adjusted font size & layout These adjustments should improve the readability of text & math.

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Pascal Michaillat

@pmichaillat

5 months

How can we deal with p-hacking? In a paper recently accepted at @restatjournal , we derive critical values that correct the inflated type 1 error rate caused by p-hacking. The paper will come out in print in 2026; meanwhile the final version is online:

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Pascal Michaillat

@pmichaillat

5 months

Just finished teaching my PhD course on economic slack at UCSC. Topics include macro models of slack, price & wage rigidity, efficiency, optimal monetary & fiscal policy over the business cycle. Lecture videos, notes, & readings are available online:

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Pascal Michaillat

@pmichaillat

1 month

Presenting at summer conferences & looking for a different LaTeX template for your slides? Or going on the job market in the fall & looking for a minimalist LaTeX template to write you job-market presentation?

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Pascal Michaillat

@pmichaillat

19 days

One thing to note: it is true that outside of growth theory, optimal control & differential equations are not used very much these days in macroeconomics. Yet they are powerful tools to obtain theoretical results not only in long-run macro but also in short-run macro.

Pascal Michaillat

@pmichaillat

21 days

Need a bit of technical support to get through first-year PhD math camp? The page hosts three short, basic notes covering mathematical methods for graduate macroeconomics: 1. Dynamic programming 2. Optimal control 3. Differential equations

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Pascal Michaillat

@pmichaillat

2 months

The US government is mandated to maintain the economy at full employment. But what is the full-employment rate of unemployment (FERU)? In this paper, which we have just revised, we argue that in the US the FERU is given by u* = √uv.

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Pascal Michaillat

@pmichaillat

2 months

It's the end of the spring quarter at UCSC! This term I was teaching a course on unemployment. Lecture videos, lecture notes, readings, & quizzes are freely available online:

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Pascal Michaillat

@pmichaillat

3 months

Looking for a template to build your personal academic website? It's completely free: it only requires Hugo and GitHub. And it's pretty user-friendly: your website should be up and running in an hour or less.

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Pascal Michaillat

@pmichaillat

2 months

Going on the job market & building your personal research website over the summer? This free & user-friendly template might be helpful: The 2024 version has improved layout, better LaTeX rendering, more social icons, etc.

GitHub - pmichaillat/hugo-website: Minimalist Hugo template for academic websites

Minimalist Hugo template for academic websites. Contribute to pmichaillat/hugo-website development by creating an account on GitHub.

github.com

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Pascal Michaillat

@pmichaillat

4 months

A new model of the divine coincidence, and of the inflation-tightness Phillips curve:

Moen Meets Rotemberg: An Earthly Model of the Divine Coincidence

This paper proposes a model of the divine coincidence, explaining its recent appearance in US data. The divine coincidence matters because it helps explain the behavior of inflation after the...

arxiv.org

Pascal Michaillat

@pmichaillat

4 months

@dandolfa Indeed, there is no connection between inflation & tightness in labor-market search models because these are real models. We have a new paper with E. Saez in which tightness (or equivalently the unemployment gap) enters the Phillips curve.

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Pascal Michaillat

@pmichaillat

21 days

The LaTeX source code is available on GitHub: This might be especially useful for people teaching related material.

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Pascal Michaillat

@pmichaillat

13 days

@wytham88 Completely agree with what you write. But I do think that LaTeX Beamer is much more convenient to write slides than PPT. I have developed this slide template to move away from the standard look and make the slides look more “rustic”:

GitHub - pmichaillat/latex-presentation: Minimalist LaTeX template for academic presentations

Minimalist LaTeX template for academic presentations - pmichaillat/latex-presentation

github.com

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Pascal Michaillat

@pmichaillat

19 days

Yet optimal control & differential equations are powerful tools to obtain analytical results in many macro models. For instance, you can use them to analyze the New Keynesian model: The analysis is short & simple.

Resolving New Keynesian Anomalies with Wealth in the Utility Function

This paper resolves the New Keynesian model's anomalies at the zero lower bound by introducing wealth in the utility function. Published in REStat, 2021.

pascalmichaillat.org

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Pascal Michaillat

@pmichaillat

3 months

The paper is now available on @restatjournal 's website: And it's open access.

Critical Values Robust to P-hacking

Abstract. P-hacking is prevalent in reality but absent from classical hypothesis-testing theory. We therefore build a model of hypothesis testing that accounts for p-hacking. From the model, we...

direct.mit.edu

Pascal Michaillat

@pmichaillat

5 months

How can we deal with p-hacking? In a paper recently accepted at @restatjournal , we derive critical values that correct the inflated type 1 error rate caused by p-hacking. The paper will come out in print in 2026; meanwhile the final version is online:

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Pascal Michaillat

@pmichaillat

2 months

@jasonfurman Hi Jason! Great point. In case that's of interest, I have a newish paper that models the winners (firm owners) and losers (incumbent workers) from immigration: The aggregate effect of immigration (in the short run) then varies over the business cycle.

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Pascal Michaillat

@pmichaillat

1 month

Here are the updated slides for our paper on u* = √uv: (Prepared for a presentation at the SF Fed—thanks to @Petrosky_Nadeau for the invitation!)

Pascal Michaillat

@pmichaillat

2 months

The US government is mandated to maintain the economy at full employment. But what is the full-employment rate of unemployment (FERU)? In this paper, which we have just revised, we argue that in the US the FERU is given by u* = √uv.

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Pascal Michaillat

@pmichaillat

1 month

Code & data for the paper are now on @github : The repo includes: - US unemployment rate, 1930–2023 - US vacancy rate, 1930–2023 - US FERU, 1930–2023 - US unemployment gap, 1930–2023 - FERU3, FERU4, FERU5 for 1994–2023 - generalized FERU for 1951–2019

GitHub - pmichaillat/feru: Code and data for the paper "u* = √uv"

Code and data for the paper "u* = √uv". Contribute to pmichaillat/feru development by creating an account on GitHub.

github.com

Pascal Michaillat

@pmichaillat

2 months

The US government is mandated to maintain the economy at full employment. But what is the full-employment rate of unemployment (FERU)? In this paper, which we have just revised, we argue that in the US the FERU is given by u* = √uv.

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20

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Pascal Michaillat

@pmichaillat

4 months

@dandolfa Indeed, there is no connection between inflation & tightness in labor-market search models because these are real models. We have a new paper with E. Saez in which tightness (or equivalently the unemployment gap) enters the Phillips curve.

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Pascal Michaillat

@pmichaillat

22 days

State of the US labor market in June 2024 (based on the analysis below):

Pascal Michaillat

@pmichaillat

2 months

The US government is mandated to maintain the economy at full employment. But what is the full-employment rate of unemployment (FERU)? In this paper, which we have just revised, we argue that in the US the FERU is given by u* = √uv.

7

20

147

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Pascal Michaillat

@pmichaillat

19 days

The paper's online appendix solves the New Keynesian model with optimal control. It also provides a heuristic derivation of the Euler equation & Phillips curve. Finally, it compares the discrete-time & continuous-time formulations of the model:

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Pascal Michaillat

@pmichaillat

5 months

P-hacking is prevalent in reality but absent from classical hypothesis-testing theory. (See for instance .) So in the paper, we build a model of hypothesis testing that accounts for p-hacking and derive critical values robust to p-hacking from it.

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Pascal Michaillat

@pmichaillat

19 days

The notes on dynamic programming are downloaded twice as often as the notes on optimal control & differential equations—a reflection of the fact that dynamic programming is much more popular in macro these days.

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Pascal Michaillat

@pmichaillat

4 months

The template is perfectly compatible with @arxiv . A paper based on the template can be submitted to arXiv in just 3 steps once it has been compiled with pdfTeX.

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Pascal Michaillat

@pmichaillat

5 months

@NatureHumBehav (The authors of the proposal include @briannosek , @CFCamerer , @guido_imbens , @econ_4_everyone , @siminevazire , @ejwagenmakers , @daddaces , @fidlerfm , @betsysinclair1 , @merliseclyde , @victoriasavalei , @trishavanzandt , and others not on Twitter.)

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Pascal Michaillat

@pmichaillat

1 month

I have updated the template in 2024 with: - New font for math symbols - New blackboard-bold font - Additional levels for lists - Customized theorems, propositions, lemmas, etc. - customized buttons The updated template offers more functionalities and should be easier to read.

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Pascal Michaillat

@pmichaillat

5 months

A very common hypothesis test is a z-test with significance level of 5%. Under the medical science calibration, the robust critical values are 2.33 if the test is one-sided & 2.58 if the test is two-sided—somewhat higher than the classical critical values of 1.64 & 1.96.

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Pascal Michaillat

@pmichaillat

5 months

@nikhildamodaran All the lectures are recorded and available online. The course webpage gives individual links. The complete playlist is at

Economic Slack

This graduate course presents various matching models of economic slack. It uses them to study business-cycle fluctuations; Keynesian, classical, and frictio...

www.youtube.com

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Pascal Michaillat

@pmichaillat

5 months

Our analysis provides a theoretical underpinning for the proposals to reduce the significance levels used in science—such as the proposal to reduce the default significance level from 5% to 0.5% by Dan Benjamin and many others in @naturehumbehav :

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Pascal Michaillat

@pmichaillat

5 months

@NatureHumBehav @BrianNosek @CFCamerer @guido_imbens @Econ_4_Everyone @siminevazire @EJWagenmakers @daddaces @fidlerfm @BetsySinclair1 @merliseclyde @VictoriaSavalei @TrishaVanZandt The tenfold reduction in the significance level that they propose is a more aggressive response to p-hacking than the fivefold reduction obtained in our baseline calibration. But it would be appropriate for a completion probability of 90%.

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Pascal Michaillat

@pmichaillat

5 months

We examine the sensitivity of the robust critical values to the calibration of the probability to complete an experiment. This probability is the key parameter of the model; its baseline calibration is 80%. We find that robust critical values are not too sensitive to it:

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Pascal Michaillat

@pmichaillat

5 months

We find that robust critical values are higher when it is easier to p-hack (for instance, when it is easier to complete experiments). This means that ideally critical values should be higher for teams with more resources & higher in fields in which running experiments is easier.

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Pascal Michaillat

@pmichaillat

2 months

@weakinstrument Thank you! Actually, as we discuss in the paper, it seems that the Fed itself has been prioritizing its inflation mandate since the 1970s. This might explain why the labor market has always been too slack in the 1970–2018 period.

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Pascal Michaillat

@pmichaillat

29 days

@KaplanEthan @restatjournal Thank you, Ethan. The aim of the paper was to solve that problem. The test will be p-hacked, but critical values are high enough such that spurious significant results do not occur more often than intended (say, no more often than 5% of the time).

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Pascal Michaillat

@pmichaillat

4 months

@dandolfa Indeed. And conversely a permanently slacker labor market results in a permanently lower inflation rate.

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Pascal Michaillat

@pmichaillat

19 days

Finally, it is easy to understand the fiscal-multiplier puzzle. You can see on the phase diagram that a small increase in the amount of government spending creates a large increase in output at the zero lower bound:

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Pascal Michaillat

@pmichaillat

5 months

@NatureHumBehav @BrianNosek @CFCamerer @guido_imbens @Econ_4_Everyone @siminevazire @EJWagenmakers @daddaces @fidlerfm @BetsySinclair1 @merliseclyde @VictoriaSavalei @TrishaVanZandt Finally, our robust critical values offer an alternative to pre-analysis plans for dealing with p-hacking. An advantage of the robust critical values is that they do not impede the process of scientific exploration & discovery.

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Pascal Michaillat

@pmichaillat

5 months

If our robust critical values are used to determine significance, and if p-hacking adjusts to the new significance standards, spurious significant results do not occur more often than purported by the significance level.

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Pascal Michaillat

@pmichaillat

5 months

Because of p-hacking, robust critical values are larger than classical critical values. In the model calibrated to medical science, the robust critical value is the classical critical value for the same test statistic but with one fifth of the significance level.

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Pascal Michaillat

@pmichaillat

5 months

@NatureHumBehav @BrianNosek @CFCamerer @guido_imbens @Econ_4_Everyone @siminevazire @EJWagenmakers @daddaces @fidlerfm @BetsySinclair1 @merliseclyde @VictoriaSavalei @TrishaVanZandt The code to produce the figures in the paper, and the exact robust critical values for all possible probabilities to complete an experiment (ease of p-hacking), are on GitHub:

GitHub - pmichaillat/p-hacking: Code and data for the paper "Critical Values Robust to P-hacking"

Code and data for the paper "Critical Values Robust to P-hacking" - pmichaillat/p-hacking

github.com

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Pascal Michaillat

@pmichaillat

2 months

A final insight from the paper is that it's possible to determine whether the economy is at full employment or not by comparing the unemployment rate u & vacancy rate v. At full employment: u = v. In general, however, the economy is too slack: u > v.

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Pascal Michaillat

@pmichaillat

2 months

@mileskimball Hi Miles, great blog post! In case that's of interest, we have a paper in which we model a psychological cost of inflation inspired by a lot of survey & experimental evidence (especially by Shiller's 1997 survey):

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Pascal Michaillat

@pmichaillat

19 days

First, it is easy to set up the New Keynesian model in continuous time. The setup of the model fits into one slide:

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Pascal Michaillat

@pmichaillat

2 months

@jasonfurman Despite the negative effect of immigration on native workers, it is optimal to allow for immigration when the labor market is too tight, such as today. The reason is that the gains in profits from immigration (from easier hiring) more than offset the losses in labor income.

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Pascal Michaillat

@pmichaillat

5 months

@steinly0 @restatjournal Yes!

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Pascal Michaillat

@pmichaillat

2 months

Since the FERU is generally lower than the actual rate of unemployment, the US economy is generally too slack. The gap between the unemployment rate & the FERU is especially large in recessions. So the US economy has generally fallen short of full employment in the past century.

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Pascal Michaillat

@pmichaillat

2 months

@dany_bahar Indeed, given the current tightness of the labor market, it is suboptimal to restrict immigration.

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Pascal Michaillat

@pmichaillat

22 days

And here is the Beveridge curve, updated to June 2024. The pre-pandemic and post-pandemic curve now overlap:

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Pascal Michaillat

@pmichaillat

4 months

@dandolfa A higher interest rate depresses aggregate demand, which reduces the demand for labor and tightness. The Fed can follow a Taylor rule or just set an interest rate peg, it doesn’t matter. The solution of the model is determinate in both cases.

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Pascal Michaillat

@pmichaillat

29 days

@KaplanEthan @restatjournal We also show that if p-hacking technology becomes better, then critical values should be raised.

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Pascal Michaillat

@pmichaillat

2 months

By extending the data to the end of 2023, it becomes even clearer how tight the post-pandemic labor market has been. The last time it was so tight was 1945—80 years ago! Given this & inflation, it is odd that the Fed did not start tightening in 2021Q2 but waited until 2022Q2.

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Pascal Michaillat

@pmichaillat

4 months

@dandolfa But the model is quite different from standard search models. In particular it requires a new pricing mechanism, blending Moen's directed search with Rotemberg's price-adjustment cost. Through this pricing mechanism tightness affects inflation.

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Pascal Michaillat

@pmichaillat

19 days

It is also easy to understand the forward-guidance puzzle. You can see on the phase diagram that a small increase in the duration of forward guidance creates a large increase in output:

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Pascal Michaillat

@pmichaillat

19 days

It is then easy to solve the household’s problem with optimal control. From there, you can study the model’s properties in normal times & at the zero lower bound using phase diagrams.

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Pascal Michaillat

@pmichaillat

19 days

The analysis offers insights that are difficult to obtain in discrete time. For instance, it is easy to understand where the collapse of output & inflation at the zero lower bound comes from.

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Pascal Michaillat

@pmichaillat

19 days

@GordonBrianR In that specific case, I think that the reason they are not used much anymore is computers. Dynamic programming and optimal control solve the same type of optimization problems, but dynamic programming is easier to solve with computers. So in the 1980s DP completely took over.

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Pascal Michaillat

@pmichaillat

3 months

@matthiaskaldorf @SamHLevey @JohnHCochrane In the past 20 years it does seem that the Phillips curve is flat when the labor market is slack: . So fiscal & monetary policy are not inflationary when the labor market is slack. We have developed a model to explain this finding:

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Pascal Michaillat

@pmichaillat

28 days

@cremieuxrecueil @uri_sohn What I was trying to say is that researchers, in our model, will not continue p-hacking once they have found a significant result because there is no benefit to having a more significant result.

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Pascal Michaillat

@pmichaillat

2 months

Between 1930 and 2023, the FERU is stable & averages 4.1%. The current value of the FERU is u* = 4.5%.

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Pascal Michaillat

@pmichaillat

28 days

@Dr_Vanitas_ @cremieuxrecueil That's correct, the proposition holds under standard OLS assumptions. It would be interesting to see how it could be extended.

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Pascal Michaillat

@pmichaillat

20 days

@policytensor The LaTeX source code to the notes is on GitHub. Feel free to fork the repository and adjust the typeface.

GitHub - pmichaillat/math-for-macro: Source files of the course "Mathematics for Macroeconomics"

Source files of the course "Mathematics for Macroeconomics" - pmichaillat/math-for-macro

github.com

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Pascal Michaillat

@pmichaillat

4 months

@dandolfa Although of course the Fed has no reason to let that happen. If the labor market is inefficiently tight and inflation is too high, the Fed should raise rates to bring everything back to normal

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Pascal Michaillat

@pmichaillat

4 months

@dandolfa Going back to your original tweet, however: you are absolutely right. Tightness does not determine inflation. Inflation and tightness are jointly determined through sellers' pricing and the Phillips curve. So the two variables move together but nothing is causal.

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Pascal Michaillat

@pmichaillat

2 months

The course was taught to advanced undergraduate students, but the material should also be appropriate for master students, & possibly for graduate students looking for not-too-technical content.

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Pascal Michaillat

@pmichaillat

3 months

@SamHLevey @darioperkins That's correct. The gap between u & v indicates an excessively tight monetary policy. We're currently adding a section to the paper to explain the sustained departure from full employment over the past century.

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Pascal Michaillat

@pmichaillat

2 months

The FERU formula u* = √uv is obtained under some simplifying assumptions. These can be relaxed to obtain a generalized formula involving social cost of unemployment, recruiting cost, & Beveridge elasticity. Quantitatively, however, the two formulas are close.

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Pascal Michaillat

@pmichaillat

28 days

@cremieuxrecueil @uri_sohn I might have misunderstood what you meant. The p-values are not all bunched at the threshold. Researchers p-hack & get random results. If a result is above the threshold they stop p-hacking. But b/c results are normally distributed, the p-values are scattered above the threshold.

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Pascal Michaillat

@pmichaillat

2 months

@jasonfurman There is actually a lot of evidence that in the short-run immigration leads to higher unemployment for incumbent workers. Most of the literature focuses on wages, which do not respond much. But in almost all studies I have seen, unemployment does go up. So there are losers here.

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Pascal Michaillat

@pmichaillat

4 months

@dandolfa The reduction of AD caused by higher rates comes through the Euler equation. The Euler equation describes people's consumption-saving decision, and as you say, it has nothing to do with tightness. The link between tightness and inflation comes through the Phillips curve.

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Pascal Michaillat

@pmichaillat

28 days

@Dr_Vanitas_ @cremieuxrecueil Online appendix C deals with the issue that you are mentioning. We show that the analysis continues to apply if researchers p-hack by cycling through various regression specifications.

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Pascal Michaillat

@pmichaillat

4 months

@hirothreading I've added some more information about the Greek letters in the documentation: Thank you for pointing this out.

Minimalist LaTeX Template for Academic Papers

This template produces an academic paper with LaTeX. The paper follows typographical best practices and has a minimalist design.

pascalmichaillat.org

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Pascal Michaillat

@pmichaillat

4 months

@dandolfa There is specific fiscal rule in the model. But I should say that the demand side and monetary policy would work exactly similarly in an NK model (as in ). What is new is the supply side and pricing mechanism.

Resolving New Keynesian Anomalies with Wealth in the Utility Function

Abstract. At the zero lower bound, the New Keynesian model predicts that output and inflation collapse to implausibly low levels and that government spending and forward guidance have implausibly...

direct.mit.edu

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Pascal Michaillat

@pmichaillat

2 months

@AxelToplitsch @just_KarlJ There is indeed a direct link between u* and r*, as we show in this related paper: