Recession Detection Using Classifiers on the Anticipation-Precision Frontier - Code and Data

This repository contains the code and data accompanying the paper "Recession Detection Using Classifiers on the Anticipation-Precision Frontier", written by Pascal Michaillat, and posted on arXiv in December 2025.

Paper webpage

The paper is available at https://pascalmichaillat.org/17/.

Overview

This project implements a machine learning approach to real-time recession detection using US labor market indicators. The methodology:

1. Constructs 95,832 recession indicators by systematically transforming unemployment and vacancy data through smoothing, curvature adjustment, turning point detection, and mixing operations
2. Identifies "perfect classifiers" that detect the correct number of recessions in a training period (1929–2021)
3. Selects optimal classifiers on the anticipation-precision frontier
4. Builds a high-precision ensemble from frontier classifiers
5. Computes recession probabilities using the ensemble's error distribution
6. Validates the approach through placebo tests and multiple backtests (1965–2015)

The approach balances early recession detection (anticipation) with consistent timing (precision), providing probabilistic assessments suitable for real-time economic monitoring.

Input data

The raw data used by the code to produce the results in the paper are stored as CSV files in the input folder.

• 20210719_cycle_dates_pasted.csv - US business cycle dates, 1857–2021
  • Source: NBER (2023)
• CLF16OV.csv - US labor force level, 1948–2025
  • Source: BLS (2025a)
• CompositeHWI.xlsx - Sheet1.csv - US vacancy rate, 1951–2020
  • Source: Barnichon (2010)
• HistoricalSeries_JME_2020January.csv - US unemployment and vacancy rates, 1890–2017
  • Source: Petrosky-Nadeau and Zhang (2021)
• INDPRO.csv - US industrial production index, 1919–2025
  • Source: Federal Reserve Board (2025)
• JTSJOL.csv - US vacancy level, 2001–2025
  • Source: BLS (2025b)
• UNEMPLOY.csv - US unemployment level, 1948–2025
  • Source: BLS (2025d)

Code

The results in the paper are obtained using MATLAB. The MATLAB code is located in the code folder.

Main script

The main script, main.m, orchestrates the production of the results in the paper. The script:

1. Loads and processes raw labor market data (1929–2025)
2. Constructs 95,832 recession indicators through systematic transformations
3. Identifies perfect classifiers on the training set (1929–2021)
4. Selects classifiers on the anticipation-precision frontier
5. Builds a high-precision ensemble
6. Computes recession probabilities
7. Performs placebo tests using First Ladies' death dates
8. Conducts backtests for 6 different training periods

Runtime

The complete script takes approximately 14–20 hours to run due to the computational intensity of the classifier selection process. Intermediate results are saved to allow partial execution.

Key functions

Data loading functions

• getUnemployment.m - Loads and splices historical unemployment data (1890–2025)
• getVacancy.m - Loads and splices historical vacancy data (1919–2025)
• getNber.m - Load and process NBER recession dates

Indicator construction functions

• buildIndicator.m - Constructs 4,356 indicators from a single time series through:
  • Smoothing: 22 methods (SMA windows 0–11 months, EMA weights 0.1–1.0)
  • Curvature: 11 Box-Cox-like transformations (0 = log, 1 = linear)
  • Turning point detection: 18 detection windows (1–18 months)
  • Total basic indicators: 22 (smoothing) × 11 (curving) × 18 (turning) = 4,356
• mixIndicator.m - Combines unemployment and vacancy indicators using linear and minmax mixing (11 mixing weights × 2 methods)
• Total indicators: 4,356 (basic indicators) × 22 (mixing) = 95,832

Classifier selection functions

• selectPerfectClassifier.m - Identifies indicator-threshold combinations that detect exactly the correct number of recessions in the training period (computationally intensive: about 2–3 hours per training period)
• selectFrontierClassifier.m - Constructs the anticipation-precision Pareto frontier by selecting classifiers that minimize mean anticipation for each precision level

Analysis functions

• computeRecessionProbability.m - Calculates recession probabilities using ensemble classifiers and their error distributions

Tabulating and plotting functions

• tabulateEnsemble.m - Creates tables of ensemble parameters and performance metrics
• plotData.m - Plots raw unemployment and vacancy rates
• plotIndicator.m - Visualizes all indicator variations
• plotFrontier.m - Shows anticipation-precision frontier
• plotEnsemble.m - Displays ensemble classifiers and thresholds
• plotProbability.m - Plots individual and aggregate recession probabilities

Utility functions

• flatten.m - Reshapes multidimensional arrays efficiently
• formatFigure.m - Configures default figure properties and defines plotting styles

Function documentation

All functions include comprehensive header documentation following MATLAB best practices:

• Syntax with all input/output arguments
• Detailed description of functionality
• Parameter specifications with units and ranges
• Usage examples
• Notes on computational requirements or special cases

Intermediate data

Some intermediate results produced by the code are saved as MATLAB files (.mat) in the intermediate folder. These results take significant time to produce (2–3 hours per file) and are provided for reference.

List of intermediate data

• ensemble.mat - Perfect classifiers for main analysis (training: 1929–2021)
• ensemble_2015.mat - Perfect classifiers for 2015 backtest
• ensemble_2005.mat - Perfect classifiers for 2005 backtest
• ensemble_1995.mat - Perfect classifiers for 1995 backtest
• ensemble_1985.mat - Perfect classifiers for 1985 backtest
• ensemble_1975.mat - Perfect classifiers for 1975 backtest - Too large for GitHub (112MB) so only available upon request
• ensemble_1965.mat - Perfect classifiers for 1965 backtest

Content of each matrix

• indexPerfect - Column indices of perfect classifiers in the indicator matrix
• thresholdPerfect - Optimal thresholds for each perfect classifier
• startPerfect - Detected recession start dates for each classifier

Usage of intermediate data

To skip the computationally intensive classifier selection step, comment the selectPerfectClassifier() and save() lines, and uncomment the appropriate load() line in main.m. This allows you to skip the selection of perfect classifiers and start analysis from the frontier selection stage. This step can also be skipped in each backtest.

Output data

The results produced by the code from the raw data are stored as PDF and CSV files in the output folder.

Figures

All figures are saved in two formats:

• PDF files - High-quality vector graphics for publication
• CSV files - Underlying data for replication or further analysis

Main analysis figures

• figure_data.pdf - Raw unemployment and vacancy rates (1929–2025)
• figure_unemployment.pdf - All 4,356 unemployment indicator variations
• figure_vacancy.pdf - All 4,356 vacancy indicator variations
• figure_frontier.pdf - Anticipation-precision frontier with all perfect classifiers
• figure_frontier_precision.pdf - Zoomed view of high-precision segment of frontier
• figure_ensemble_[1-N].pdf - Individual ensemble classifier plots
• figure_ensemble.pdf - Combined plot of normalized ensemble classifiers
• figure_probability_training.pdf - Recession probabilities on training period
• figure_probability_testing.pdf - Recession probabilities on testing period

Placebo test figures

• figure_frontier_placebo.pdf - Anticipation-precision frontier using First Ladies' death dates for placebo test

Backtest figures

For each backtest year (2015, 2005, 1995, 1985, 1975, 1965):

• figure_frontier_[year].pdf - Frontier for that training period
• figure_frontier_[year]_precision.pdf - Zoomed frontier view
• figure_ensemble_[year]_[1-N].pdf - Individual classifiers
• figure_ensemble_[year].pdf - Combined ensemble
• figure_probability_[year]_training.pdf - Recession probabilities on training period
• figure_probability_[year]_testing.pdf - Recession probabilities on backtesting period

Tables

All tables are saved as CSV files with complete parameter specifications and performance metrics.

Main analysis tables

• table_ensemble.csv - Classifier ensemble parameters and errors. Columns: Smoothing method, smoothing parameter, curving parameter, turning parameter, mixing method, mixing parameter, threshold, standard error, mean error, min error, max error

Placebo test tables

• table_ensemble_placebo.csv - Frontier classifiers for the placebo test

Backtest tables

For each backtest year:

• table_ensemble_[year].csv - Classifier ensemble parameters and errors for that backtest

Usage

Prerequisites

• MATLAB R2019b or later (some functions require recent MATLAB features)
• Sufficient memory for large matrix operations (16GB+ RAM recommended)
• Approximately 10GB free disk space for intermediate and output files

Running the analysis

1. Clone the repository to your local machine using Git or by downloading the ZIP file:

git clone https://github.com/pmichaillat/recession-detection.git

2. Open MATLAB and set the code folder as the current folder.

3. To generate all the results, run the following command in the MATLAB command window:

run('main.m')

4. By default, the main script overwrites the files in the intermediate and output folders. To preserve existing files, make a copy of the folders before running the script.

5. Important note: The script takes 14–20 hours to run completely due to classifier selection. Progress is displayed in the command window.

Partial execution

To skip the computationally intensive selection of perfect classifiers, use pre-computed results:

1. Ensure intermediate .mat files exist in intermediate/.

2. In main.m, comment the selectPerfectClassifier() and save() lines, and uncomment the appropriate load() line in main.m. This allows you to skip the selection of perfect classifiers and start analysis from the frontier selection stage. This step can also be skipped in each backtest.

3. Run the main.m script. It will use saved classifiers instead of recomputing them.

Customization

Modify training period

• Edit beginTraining and endTraining in main.m

Adjust ensemble precision threshold

• Modify stdErrorMax in main.m
• Lower values = more precise but fewer classifiers
• Higher values = more classifiers but less precise

Change backtest periods

• Edit the backtest year array in main.m
• Add or remove years as desired

Customize figure formatting

• Modify properties in formatFigure.m
• Adjust colors, line widths, fonts, etc.

Software

The results were obtained using MATLAB R2024b on macOS Tahoe (Apple silicon). The code should work on:

• MATLAB R2019b or later
• Windows, macOS, or Linux
• Both Intel and Apple silicon processors
• No required toolboxes. All code uses base MATLAB functions.

License

This repository is licensed under the MIT License.