Beveridgean Unemployment Gap: Code and Data

This repository contains the code and data accompanying the paper "Beveridgean Unemployment Gap", written by Pascal Michaillat and Emmanuel Saez, and published in the Journal of Public Economics Plus in November 2021.

Paper webpage

The paper and its online appendix are available at https://pascalmichaillat.org/9/.

Data

The data used as input to produce the results in the article are stored in the Excel file data.xlsx, which is placed in the folder code.

Code

The results in the paper are produced with MATLAB code. The code is placed in the folder code. There are two types of programs:

1. MATLAB scripts producing the figures in the article and online appendix
2. MATLAB helper scripts and functions called at different places by the figure-producing scripts

Figure-producing scripts

The figures in the article and online appendix are produced by the following scripts:

• figure1A.m - Produce figure 1A
• figure1B.m - Produce figure 1B
• figure1CF.m - Produce figures 1C, 1D, 1E, 1F
• figure5.m - Produce figures 5A, 5B, 5C, 5D, 5E, 5F
• figure6.m - Produce figure 6
• figure7A.m - Produce figure 7A
• figure7B.m - Produce figure 7B
• figure7C.m - Produce figure 7C
• figure7D.m - Produce figure 7D
• figure8A.m - Produce figure 8A
• figure8B.m - Produce figure 8B
• figure8C.m - Produce figure 8C
• figure9A.m - Produce figure 9A
• figure9B.m - Produce figure 9B
• figure9C.m - Produce figure 9C
• figure10.m - Produce figure 10
• figureA1.m - Produce figure A1
• figureA2.m - Produce figure A2
• figureA3.m - Produce figure A3
• figureA4.m - Produce figure A4
• figureA5.m - Produce figure A5
• figureA6.m - Produce figure A6
• figureA7.m - Produce figure A7
• figureA8.m - Produce panels A and B or figure A8
• figureA9.m - Produce figure A9

The scripts produce each figure in a MATLAB window, save a copy of each figure in PDF format, and save a copy of the data plotted in each figure in an Excel file.

Helper scripts and functions

The figure-producing scripts call the following helper scripts:

• formatFigure.m - Format figures
• formatPlot.m - Provide formatting settings for plots

The figure-producing scripts also call the following functions:

• computeBeveridgeanUnemployment.m - Compute Beveridgean unemployment rate in DMP model
• computeBeveridgeInverse.m - Compute inverse-optimum Beveridge elasticity from sufficient-statistic formula
• computeEfficiencyEndogenous.m - Compute efficient allocation in DMP model using sufficient-statistic formula with endogeous Beveridge elasticity
• computeEfficiencyHosios.m - Compute efficient allocation in DMP model using Hosios condition
• computeEfficientTightness.m - Compute efficient labor-market tightness from sufficient-statistic formula
• computeEfficientUnemployment.m - Compute efficient unemployment rate from sufficient-statistic formula
• computeMatchingEfficacy.m - Compute matching efficacy in DMP model
• computeMatchingElasticity.m - Compute matching elasticity in DMP model
• computeNonworkInverse.m - Compute inverse-optimum social value of nonwork from sufficient-statistic formula
• computeRecruitingInverse.m - Compute inverse-optimum recruiting cost from sufficient-statistic formula
• computeSeparationEfficacy.m - Compute separation-efficacy ratio in DMP model
• computeUnemploymentGap.m - Compute unemployment gap from sufficient-statistic formula
• getBeveridgeElasticity.m - Return Beveridge elasticity in the United States, 1951–2019
• getBreakDate.m - Return dates of structural breaks in US Beveridge curve between 1951 and 2019
• getLaborProductivity.m - Return quarterly labor productivity in the United States, 1951–2019
• getNairu.m - Return NAIRU in the United States, 1960Q1–2018Q3
• getNaturalUnemployment.m - Return natural rate of unemployment in the United States, 1951–2019
• getRecessionDate.m - Return dates of recessions in the United States between 1951 and 2019
• getTimeline.m - Return quarterly timeline for 1951Q1–2019Q4
• getTrendUnemployment.m - Return trend of unemployment rate in the United States, 1960Q1–2018Q3
• getUnemploymentRate.m - Return quarterly unemployment rate in the United States, 1951–2019
• getVacancyRate.m - Return quarterly vacancy rate in the United States, 1951–2019
• measureJobFinding.m - Measure job-finding rate in the United States, 1951–2019
• measureJobSeparation.m - Measure job-separation rate in the United States, 1951–2019
• monthlyToQuarterly.m - Aggregate monthly data to quarterly frequency

A last helper script is baiPerron.m. This MATLAB script estimates the US Beveridge curve with the Bai-Perron algorithm. It calls on MATLAB functions stored in the folder baiperron. The folder was created by Yohei Yamamoto, based on Gauss code by Pierre Perron. It was downloaded from http://blogs.bu.edu/perron/files/2020/05/m-break-matlab.zip.

Figures

The figures produced by the code are stored in the folder figures, both as PDF files and as Excel files.

PDF files

The figures produced by the code are saved as PDF files and stored in the subfolder pdf. The PDF files correspond to the following figures in the article and online appendix:

• figure1A.pdf - Figure 1A
• figure1B.pdf - Figure 1B
• figure1C.pdf - Figure 1C
• figure1D.pdf - Figure 1D
• figure1E.pdf - Figure 1E
• figure1F.pdf - Figure 1F
• figure5A.pdf - Figure 5A
• figure5B.pdf - Figure 5B
• figure5C.pdf - Figure 5C
• figure5D.pdf - Figure 5D
• figure5E.pdf - Figure 5E
• figure5F.pdf - Figure 5F
• figure6.pdf - Figure 6
• figure7A.pdf - Figure 7A
• figure7B.pdf - Figure 7B
• figure7C.pdf - Figure 7C
• figure7D.pdf - Figure 7D
• figure8A.pdf - Figure 8A
• figure8B.pdf - Figure 8B
• figure8C.pdf - Figure 8C
• figure9A.pdf - Figure 9A
• figure9B.pdf - Figure 9B
• figure9C.pdf - Figure 9C
• figure10.pdf - Figure 10
• figureA1.pdf - Figure A1
• figureA2.pdf - Figure A2
• figureA3.pdf - Figure A3
• figureA4.pdf - Figure A4
• figureA5.pdf - Figure A5
• figureA6.pdf - Figure A6
• figureA7.pdf - Figure A7
• figureA8A.pdf - Panel A of figure A8
• figureA8B.pdf - Panel B of figure A8
• figureA9.pdf - Figure A9

Excel files

The data underlying all the figures produced by the code are saved as Excel files and stored in the subfolder xlsx. The Excel files contain data pertaining to the following figures in the article and online appendix:

• figure1A.xlsx - Figure 1A
• figure1B.xlsx - Figure 1B
• figure1CF.xlsx - Figures 1C, 1D, 1E, 1F
• figure5.xlsx - Figures 5A, 5B, 5C, 5D, 5E, 5F
• figure6.xlsx - Figure 6
• figure7A.xlsx - Figure 7A
• figure7B.xlsx - Figure 7B
• figure7C.xlsx - Figure 7C
• figure7D.xlsx - Figure 7D
• figure8A.xlsx - Figure 8A
• figure8B.xlsx - Figure 8B
• figure8C.xlsx - Figure 8C
• figure9A.xlsx - Figure 9A
• figure9B.xlsx - Figure 9B
• figure9C.xlsx - Figure 9C
• figure10.xlsx - Figure 10
• figureA1.xlsx - Figure A1
• figureA2.xlsx - Figure A2
• figureA3.xlsx - Figure A3
• figureA4.xlsx - Figure A4
• figureA5.xlsx - Figure A5
• figureA6.xlsx - Figure A6
• figureA7.xlsx - Figure A7
• figureA8.xlsx - Panels A and B of figure A8
• figureA9.xlsx - Figure A9

The subfolder xlsx also contains the output of the Bai-Perron algorithm produced by the script baiperron.m. The output is saved as a text file: baiperron.txt.

Software

The results were obtained on a Mac running macOS BigSur 11.6 with MATLAB R2021a and Microsoft Excel 16.54.

License

The content of this repository is licensed under the terms of the MIT License.

Related code

• Python version of this code – Written by Sarah Charlton. All the paper's results are presented in Jupyter Notebooks.