Equilibrium Transport

Packages

We use POT for optimal transport in one period. The implementations of Jenks natural breaks and total variation denoising in 1d are based on other authors' work, given in the files jenks.py and tv1d.py.

Thanks to the authors of these packages!

Usage

Code for two job markets is given in two folders Executives and California, which can work separately.

Illustrative examples

MV_precommit.py and MV_equilibrium.py are for the toy example on dynamic matching between supply and demand.

Executives

Data

With access to WRDS, we download financial statements data from Compustat North America and executive compensation data from Execucomp.

In Compustat, we choose the following query variables. For five-year data, set the date as 2017 to 2022. Name the output file as finstat_y17.csv.

• Global Company Key (GVKEY)
• Ticker Symbol (TIC)
• GIC Groups (GGROUP)
• GIC Industries (GIND)
• GIC Sectors (GSECTOR)
• GIC Sub-Industries (GSUBIND)
• Data Year Fiscal (FYEAR)
• Sales/Turnover (Net) (SALE)
• Market Value Total Fiscal (MKVALT)

In Execucomp, we choose the following query variables. For five-year data, set the date as 2017 to 2022. Name the output file as ceo_y17.csv.

• Compustat's Global Company Key (GVKEY)
• (Current) Ticker Symbol (TICKER)
• EXEC_FULLNAME (EXEC_FULLNAME)
• Date Became CEO (BECAMECEO)
• Title (TITLE)
• Total Compensation (Salary + Bonus + Others) (TDC1)
• Year (YEAR)

Credit rating data are obtained from Compustat Daily Updates - Ratings on date 2017-01 only. Name the output file as rating_y17.csv. Variables include

• Company Name (CONM)
• Ticker Symbol (TIC)
• CUSIP (CUSIP)
• S&P Domestic Long Term Issuer Credit Rating (SPLTICRM)
• S&P Subordinated Debt Rating (SPSDRM)
• S&P Domestic Short Term Issuer Credit Rating (SPSTICRM)

For validation, 790firms_gvkey.txt gives the GVKEY of 790 firms after cleaning 2017-2021 data. Readers can also use this file in WRDS queries.

Replication steps

1. With data obtained, use CleanData_5Years.ipynb to clean and merge data. The output is merged_y17_avgmanager.csv.
2. Select a suitable number of groups with GroupNumberSelection.py. There are two flag variables, search_mode and even_split. If search_mode is true, it will consider all candidates of group numbers and generate correlation pickle files to plot the group number screening figure. If search_mode is false, only one candidate of group numbers is used and it generates data files called classified_group_{}.csv and wage_beta_group_{}.csv. even_split controls whether to use even splits.
3. Estimate transition matrices. We need to download the data for a longer time horizon such as 2000-2022. Name the output files from WRDS as ceo_20years.csv and finstat_20years.csv. Then clean the data with CleanData_12Years_TransMat.py and remember to set n_group as the one obtained from Step 2. Next, run Calc_TransMatrix.py with the same n_group to estimate transition matrices.
4. Executives_equi.py calculates theoretical equilibrium transport with different alphas. The flag variable bench_zero means to use perfectly matched data (=True) or bootstrap real data (=False). Also, set n_groups the same as above.
5. Executives_cali.py generates the Sinkhorn distances between theoretical and real transport plans. Variables bench_zero and n_groups should be the same as in Step 4.
6. Figures and tables are obtained by Tables_Statistics.ipynb and Tables_Executives_Alpha.ipynb.

California

Data

The University of California (UC) Compensation data are from Government Compensation in California website. Put 2013-2021 files into a folder called UniversityOfCalifornia. The dataset in the Year 2013 uses different job titles. For example, 'Assoc Prof-Ay-B/E/E' is called 'Associate Prof-Ay-B/E/E'. We use Clean_Y2013_Data.ipynb to unify the job titles. US News Rankings are obtained from Andrew G. Reiter's website. We have added USNews_Ranking.csv for readers' reference.

Clean_UC_Salary.ipynb cleans and merges compensations and rankings data. Readers can also use the output uc_salary.csv directly. Wages are also rankings in this file.

Replication steps

1. Estimate transition matrices with UC_transmatrix.py.
2. Similarly, UC_equi.py calculates theoretical equilibrium transport with different alphas. The flag variable bench_zero means to use perfectly matched data (=True) or bootstrap real data (=False).
3. UC_cali.py generates the Sinkhorn distances between theoretical and real transport plans. Variables bench_zero should be the same as in Step 2.
4. Figures and tables are obtained by Results_Figs_Tables.ipynb and Descriptive_Statistics.ipynb.