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https://github.com/pmichaillat/unemployment-gap

Code and data for the paper "Beveridgean Unemployment Gap"
https://github.com/pmichaillat/unemployment-gap

beveridge-curve business-cycles efficient-unemployment labor-market-tightness paper-with-code sufficient-statistics unemployment-gap

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Code and data for the paper "Beveridgean Unemployment Gap"

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# Beveridgean Unemployment Gap: Code and Data



This repository contains the code and data accompanying the paper "Beveridgean Unemployment Gap", written by [Pascal Michaillat](https://pascalmichaillat.org) and [Emmanuel Saez](https://eml.berkeley.edu/~saez/), and published in the [Journal of Public Economics Plus](https://doi.org/10.1016/j.pubecp.2021.100009) in December 2021.



## Paper webpage



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



## Data



The data used to produce the results in the article are placed in the folder `data`. The data used as input by the code are stored in the Excel file `data.xlsx`. The data from the 1997 National Employer Survey (NES) are placed in the subfolder `nes`:



+ `nes.csv` – Public-use CSV file of the 1997 NES; the recruiting cost in the United States is computed from the answer to question 29

+ `questionaire.pdf` – Questionaire of the 1997 NES

+ `description.pdf` – Description of the NES data by Peter Cappelli (principal investigator of the 1997 NES)



## Code



The code used to produce the results in the paper is placed in the folder `code`. 

The code is written in MATLAB. 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, 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](https://github.com/smxzehvb/unemployment-gap/tree/main/python) – Written by Sarah Charlton. All the paper's results are presented in Jupyter Notebooks.