This repository contains the code and data accompanying the paper "u* = √uv: The Full-Employment Rate of Unemployment in the United States", written by Pascal Michaillat and Emmanuel Saez, and to be published in the Fall 2024 issue of Brookings Papers on Economic Activity.
The paper is available at https://pascalmichaillat.org/13/.
The raw data used by the code to produce the results in the paper are stored as CSV files. The data are placed in the raw folder.
20210719_cycle_dates_pasted.csv– US recession dates, 1930–2024CLF16OV.csv– US labor force level, 1948–2024CompositeHWI.xlsx - Sheet1.csv– US vacancy rate, 1951–2020- Source: Barnichon (2010)
ustar.csv– US NAIRU, 1960–2023figure5.csv– Dates of structural breaks in the US Beveridge curve, 1951–2019- Source: Michaillat and Saez (2021a)
figure6.csv– Elasticity of the US Beveridge curve, 1951–2019- Source: Michaillat and Saez (2021a)
HistoricalSeries_JME_2020January.csv– US unemployment and vacancy rates, 1890–2017- Source: Petrosky-Nadeau and Zhang (2021)
JTSJOL.csv– Job openings in the United States, 2001–2024LNU05026642.csv– Marginally attached workers in the United States, 1994–2024LNU05026645.csv– Discouraged workers in the United States, 1994–2024NROU.csv– US NRU, 1949–2024NROUST.csv– US short-term NRU, 1949–2021U4RATE.csv– US U4 unemployment rate, 1994–2024U5RATE.csv– US U5 unemployment rate, 1994–2024UNRATE.csv– US unemployment (U3) rate, 1948–2024
The results in the paper are produced with MATLAB code. The code is placed in the code folder.
The main script, main.m, orchestrates the production of the results in the paper:
- The script produces the 30 figures presented in the paper. The script generates each figure in a figure window and saves the figures as PDF files. The script saves the data used to generate each figure in CSV files.
- The script also produces the numerical results associated with each figure. The results are displayed in the command window and saved in Markdown files.
Before the computations begin, the main script calls the script formatFigure.m to preformat figures and predefine plot properties.
The main script then produces the individual figures using a collection of scripts:
figure1A.m– Produce panel A of figure 1figure1B.m– Produce panel B of figure 1figure2.m– Produce panels A, B, C, D, E, and F of figure 2figure3A.m– Produce panel A of figure 3figure3B.m– Produce panel B of figure 3figure4A.m– Produce panel A of figure 4figure4B.m– Produce panel B of figure 4figure5A.m– Produce panel A of figure 5figure5B.m– Produce panel B of figure 5figure6A.m– Produce panel A of figure 6figure6B.m– Produce panel B of figure 6figure7A.m– Produce panel A of figure 7figure7B.m– Produce panel B of figure 7figure8A.m– Produce panel A of figure 8figure8B.m– Produce panel B of figure 8figure9A.m– Produce panel A of figure 9figure9B.m– Produce panel B of figure 9figure10.m– Produce figure 10figure11.m– Produce figure 11figure12.m– Produce figure 12figure13A.m– Produce panel A of figure 13figure13B.m– Produce panel B of figure 13figure14A.m– Produce panel A of figure 14figure14B.m– Produce panel B of figure 14figure15.m– Produce figure 15
The scripts produce figures in figure windows, save a copy of each figure in PDF format, and save the data used to generate each figure in CSV files. Each script also produces the numerical results associated with the figure. The results are displayed in the command window and saved in a Markdown file.
The production scripts rely on a collection of helper functions:
getBreak– Return dates of structural breaks of the US Beveridge curve, 1951–2019getData345– Return US U3, U4, U5 unemployment rates, 1994–2024getElasticity– Return elasticity of the US Beveridge curve, 1951–2019getNairu– Return US NAIRU, 1960–2023getNru– Return US NRU, 1949–2024getNrust– Return US short-term NRU, 1949–2021getRecession.m– Return US recession dates, 1930–2024getRecession345– Return US recession dates, 1994–2024getRecessionDepression.m– Return US recession dates, 1930–1950getRecessionPandemic.m– Return US recession dates, 2020–2024getRecessionPostwar.m– Return US recession dates, 1951–2019getUnemployment.m– Return US unemployment rate, 1930–2024getUnemploymentDepression.m– Return US unemployment rate, 1930–1950getUnemploymentJolts.m– Return US unemployment rate, 2001–2024getUnemploymentPandemic.m– Return US unemployment rate, 2020–2024getUnemploymentPostwar.m– Return US unemployment rate, 1951–2019getVacancy.m– Return US vacancy rate, 1930–2024getVacancyDepression.m– Return US vacancy rate, 1930–2024getVacancyJolts.m– Return US vacancy rate, 2001–2024getVacancyPandemic.m– Return US vacancy rate, 2020–2024getVacancyPostwar.m– Return US vacancy rate, 1951–2019monthly2quarterly.m– Convert monthly data to quarterly data
The 30 figures produced by the code are saved as 30 PDF files. The data used to generate each figure are saved in CSV files. And the numerical results associated with each figure are saved in Markdown files. All these files are placed in the figures folder, each corresponding to a specific figure in the paper:
figure1A.pdf,figure1A.csv,figure1A.md– Panel A of figure 1figure1B.pdf,figure1B.csv– Panel B of figure 1figure2A.pdf,figure2.csv– Panel A of figure 2figure2B.pdf,figure2.csv– Panel B of figure 2figure2C.pdf,figure2.csv– Panel C of Figure 2figure2D.pdf,figure2.csv– Panel D of Figure 2figure2E.pdf,figure2.csv– Panel E of Figure 2figure2F.pdf,figure2.csv– Panel F of Figure 2figure3A.pdf,figure3A.csv– Panel A of figure 3figure3B.pdf,figure3B.csv,figure3B.md– Panel B of figure 3figure4A.pdf,figure4A.csv,figure4A.md– Panel A of figure 4figure4B.pdf,figure4B.csv,figure4B.md– Panel B of figure 4figure5A.pdf,figure5A.csv,figure5A.md– Panel A of figure 5figure5B.pdf,figure5B.csv,figure5B.md– Panel B of figure 5figure6A.pdf,figure6A.csv– Panel A of figure 6figure6B.pdf,figure6B.csv,figure6B.md– Panel B of figure 6figure7A.pdf,figure7A.csv,figure7A.md– Panel A of figure 7figure7B.pdf,figure7B.csv,figure7B.md– Panel B of figure 7figure8A.pdf,figure8A.csv,figure8A.md– Panel A of figure 8figure8B.pdf,figure8B.csv,figure8B.md– Panel B of figure 8figure9A.pdf,figure9A.csv,figure9A.md– Panel A of figure 9figure9B.pdf,figure9B.csv,figure9B.md– Panel B of figure 9figure10.pdf,figure10.csv– Figure 10figure11.pdf,figure11.csv,figure11.md– Figure 11figure12.pdf,figure12.csv,figure12.md– Figure 12figure13A.pdf,figure13A.csv,figure13A.md– Panel A of figure 13figure13B.pdf,figure13B.csv,figure13B.md– Panel B of figure 13figure14A.pdf,figure14A.csv,figure14A.md– Panel A of figure 14figure14B.pdf,figure14B.csv,figure14B.md– Panel B of figure 14figure15.pdf,figure15.csv,figure15.md– Figure 15
To generate all figures and numerical results presented in the paper, run the following command in MATLAB:
run('main.m')Before running the script, ensure you save a copy of the figures folder, as all files in that folder will be overwritten by the code when new figures are generated.
Alternatively, you can save the new files produced by the code in a new folder. To do this, create a new folder newfigures, and then in main.m, adjust the output folder with the following line:
outputFolder = fullfile('..', 'newfigures');The results were obtained using MATLAB R2024a on an Apple Silicon Mac running macOS Sequoia 15.0. In MATLAB, the Statistics and Machine Learning Toolbox is required to run some of the scripts.
The content of this repository is licensed under the terms of the MIT License.