This is the replication package for my paper "Firm Dynamics and Random Search over the Business Cycle" published in the Journal of Monetary Economics [doi].

If you find this package helpful in your work, please consider citing the paper:

@article{audoly2026firm,
  author  = {Audoly, Richard},
  title   = {{Firm Dynamics and Random Search over the Business Cycle}},
  journal = {Journal of Monetary Economics},
  volume  = {158},
  pages   = {103902},
  year    = {2026},
  doi     = {10.1016/j.jmoneco.2026.103902}
}

• code/: replication scripts
• data/: replication input data and intermediate artifacts
• figures/: final figures produced by replication scripts [created by running the code]
• tables/: final tables produced by replication scripts [created by running the code]

• Stata (last run on Stata/SE 18)
• MATLAB (last run on R2023a)
  • The figure scripts call recessionplot, which is provided by the MATLAB Econometrics Toolbox.

• Step 1: Firm-level micro data
• Step 2: Time series data
• Step 3: Solve and simulate alternative models
• Step 4: Generate figures and tables

This step derives several key statistics from confidential British firm-level data.

The raw firm-level data is confidential and cannot be shared. Access can be requested from the UK Data Service.

The relevant datasets are:

• Business Structure Database (BSD): http://doi.org/10.5255/UKDA-SN-6697-10
• Annual Business Survey (ABS): http://doi.org/10.5255/UKDA-SN-7451-15
• Annual Respondents Database (ARD): http://doi.org/10.5255/UKDA-SN-6644-5

Scripts are located in code/step1_firm_micro_data/. The scripts do not need to be run to reproduce the paper.

The moments and time series derived from this step are already included in the replication package given the confidential nature of the underlying data. The scripts do not need to be run to reproduce the paper.

This step constructs the time-series inputs used by the model code.

• data/time_series/raw/
  • Raw ONS/BHPS/ABS/BSD inputs used to construct macro series.
• data/time_series/recessions_uk/
  • dates.csv
  • quarters.csv

Scripts are located in code/step2_time_series_data/:

• clean_series.do
  • Reads raw inputs and constructs monthly/quarterly/yearly series in Stata format.
• detrend_series.do
  • Applies detrending (HP and band-pass filters) and exports the detrended series used by the model.
  • Removes intermediate Stata .dta artifacts after exporting the final .csv files.
• prepare_model_series.m
  • Interpolates the yearly detrended series to a monthly frequency and exports monthly_series.csv.

Run from the code/step2_time_series_data/ folder.

1. Stata:

   • Run clean_series.do
   • Run detrend_series.do

2. MATLAB:

   • Run prepare_model_series.m

These files are created under data/time_series/detrended/:

• quarterly_series.csv
• yearly_series.csv
• monthly_series.csv

This step solves and simulates alternative model specifications and stores the solution and simulation output used to generate paper figures and tables. The code will take several hours to run.

• data/model_parameters/
  • Calibration inputs for the steady state and aggregate shocks.
• data/time_series/detrended/monthly_series.csv
  • Constructed in Step 2.

Scripts are located in code/step3_model_solutions_simulations/:

• aggregate_shocks_simulations.m
  • Solves for multiple model configurations.
  • Simulates business cycles and finds sequences of shocks matching target data series.
  • Saves solutions to data/model_solutions/ and simulations to data/model_simulations/.

Run from the code/step3_model_solutions_simulations/ folder.

• MATLAB:
  • Run aggregate_shocks_simulations.m

This script writes under data/:

• data/model_solutions/<model_type>/
  • Solution objects (e.g., theta_<steady_state>_<aggregate_shocks>).
• data/model_simulations/<model_type>/
  • Simulation output files named <steady_state>_<aggregate_shocks>.mat (stored as simulation_output).

This step generates the final figures and tables using the time series (Step 2) and model simulation output (Step 3).

• data/time_series/detrended/
  • monthly_series.csv
  • yearly_series.csv
• data/time_series/recessions_uk/dates.csv
• data/model_simulations/
  • Simulation output files produced in Step 3.
• data/model_parameters/
  • Used to re-solve steady-state models for some tables.

Scripts are located in code/step4_figures_and_tables/:

• fig1.m
• fig2.m
• tab1.m
• tab2.m
• tab3.m

Run from the code/step4_figures_and_tables/ folder.

• MATLAB:
  • Run fig1.m
  • Run fig2.m
  • Run tab1.m
  • Run tab2.m
  • Run tab3.m

These files are created under figures/:

• fig1a.*, fig1b.*, fig1c.*, fig1d.*, fig1e.*, fig1f.*
• fig2a.*, fig2b.*, fig2c.*, fig2d.*

The file extension is controlled by the MATLAB figure_options() helper.

These files are created under tables/:

• tab1.txt
• tab2.txt
• tab3.txt