u* = √uv : Code and Data

This repository contains the code and data accompanying the paper "u* = √uv", written by Pascal Michaillat and Emmanuel Saez, and posted on arXiv in June 2022.

Paper webpage

The paper is available at https://pascalmichaillat.org/13/.

Data

The data used as input to produce the results in the paper 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 paper
2. MATLAB helper scripts and functions called by the figure-producing scripts

Figure-producing scripts

The figures in the paper are produced by the following scripts:

• figure1A.m – Produce figure 1A
• figure1B.m – Produce figure 1B
• figure3A.m – Produce figure 3A
• figure3B.m – Produce figure 3B
• figure4A.m – Produce figure 4A
• figure4B.m – Produce figure 4B
• figure5.m – Produce figure 5
• figure6A.m – Produce figure 6A
• figure6B.m – Produce figure 6B
• figure7A.m – Produce figure 7A
• figure7B.m – Produce figure 7B
• figure8.m – Produce figure 8
• figure9A.m – Produce figure 9A
• figure9B.m – Produce figure 9B
• figure10A.m – Produce figure 10A
• figure10B.m – Produce figure 10B
• figure11A.m – Produce figure 11A
• figure11B.m – Produce figure 11B
• figure12A.m – Produce figure 12A
• figure12B.m – Produce figure 12B
• figure12C.m – Produce figure 12C

Each script produces a figure in a MATLAB window, saves a copy of the figure in PDF format, and saves a copy of the data plotted in the figure in an Excel file.

Figure 2 is directly borrowed from Michaillat and Saez (2021, figure 5), so there is no script to produce it.

Helper scripts and functions

The figure-producing scripts call the following helper scripts:

• formatStandardPlot.m – Format standard plots
• formatScatterPlot.m – Format scatter plots
• formatLongPlot.m – Format long plots

The figure-producing scripts also call the following functions:

• getRecession.m – Return dates of US recessions between 1930Q1 and 2022Q1
• getRecessionDepression.m – Return dates of US recessions between 1930Q1 and 1950Q4
• getRecessionPostwar.m – Return dates of US recessions between 1951Q1 and 2019Q4
• getRecessionPandemic.m – Return dates of US recessions between 2020M1 and 2022M3
• getTimeline.m – Return quarterly timeline for 1930Q1–2022Q1
• getTimelineDepression.m – Return quarterly timeline for 1930Q1–1950Q4
• getTimelinePostwar.m – Return quarterly timeline for 1951Q1–2019Q4
• getTimelinePandemic.m – Return monthly timeline for 2020M1–2022M3
• getTimelineJolts.m – Return monthly timeline for 2001M1–2022M3
• getUnemployment.m – Return quarterly US unemployment rate, 1930Q1–2022Q1
• getUnemploymentDepression.m – Return quarterly US unemployment rate, 1930Q1–1950Q4
• getUnemploymentPostwar.m – Return quarterly US unemployment rate, 1951Q1–2019Q4
• getUnemploymentPandemic.m – Return monthly US unemployment rate, 2020M1–2022M3
• getUnemploymentJolts.m – Return monthly US unemployment rate, 2001M1–2022M3
• getUnemploymentMS21.m – Return the efficient unemployment rate by Michaillat and Saez (2021)
• getVacancyRate.m – Return quarterly US vacancy rate, 1930Q1–2022Q1
• getVacancyRateDepression.m – Return quarterly US vacancy rate, 1930Q1–1950Q4
• getVacancyRatePostwar.m – Return quarterly US vacancy rate, 1951Q1–2019Q4
• getVacancyRatePandemic.m – Return monthly US vacancy rate, 2020M1–2022M3
• getVacancyRateJolts.m – Return monthly US vacancy rate, 2001M1–2022M3
• monthlyToQuarterly.m – Aggregate monthly data to quarterly frequency

Figures

The 21 figures produced by the code are stored both as PDF files and as Excel files. The figures are placed in the folder figures.

PDF files

The figures are saved as PDF files and stored in the subfolder pdf. Any PDF file titled figureX.pdf corresponds to figure X in the paper.

Excel files

The data underlying the figures are saved as Excel files and stored in the subfolder xlsx. Any Excel file titled figureX.xlsx contains the data plotted in figure X in the paper.

Software

The results were obtained on a Mac running macOS Ventura 13.2 with MATLAB R2022b and Microsoft Excel 16.71.

License

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