PyXthreg: High-Performance Panel Threshold Regression in Python

pyxthreg is a highly optimized Python package for estimating fixed-effects panel threshold models, originally pioneered by Hansen (1999).

Built from the ground up for massive empirical datasets, it replicates the mathematical exactness of the historical Stata module xthreg (Wang, 2015) while delivering a multifold speedup by circumventing the Python Global Interpreter Lock (GIL) via JIT compilation (Numba) and multi-core parallelization.

Ideal for applied econometrics and macroeconomic research, this package modernizes regime-switching modeling within the Python data science ecosystem.

🌟 Key Features

• Absolute Stata Parity: Replicates point estimates, standard errors, and Hansen's sequential Likelihood Ratio (LR) bootstrap tests with exact mathematical precision.
• Autonomous Regime Discovery: Features an intelligent sequential algorithm (thnum="auto") that dynamically searches for an arbitrary number of $K$ thresholds, strictly halting when additional structural breaks lose statistical significance.
• Massive Speedup (Numba JIT): Executes the computationally heavy residual-based bootstrap iterations concurrently across all available CPU cores, reducing execution times from hours to seconds.
• Native Robust Inference: Supports cluster-robust Sandwich variance-covariance estimators (robust=True) to seamlessly correct for heteroskedasticity and intra-group serial correlation.
• Memory-Efficient Fixed Effects: Natively applies a two-way partial within-transformation (time_fe=True) via the Frisch-Waugh-Lovell theorem, avoiding the creation of memory-heavy dummy variables.
• Publication-Ready Visualizations: Built-in methods to generate the classic Hansen LR V-shaped confidence intervals, SSR evolution plots, and dynamic regime transition charts.

📦 Installation

The stable release is available on the Python Package Index (PyPI). Install it using pip:

pip install pyxthreg

Development install from source:

git clone https://github.com/Kahindo048/pyxthreg.git
cd pyxthreg
pip install -e .

🚀 Quick Start

The API is designed to be intuitive and strictly requires a standard "long format" pandas DataFrame.

import pandas as pd
from pyxthreg import ThresholdPanel
from pyxthreg.load_data import load_dataset

# ==========================================
# 1. DATA LOADING
# ==========================================
# Using the package's utility function to load the test panel.
# This dataset contains a strongly balanced panel.
try:
    df = load_dataset("model_1.dta")
    print(f"Data loaded successfully: {df.shape[0]} observations.")
except FileNotFoundError:
    print("Error: The file 'model_1.dta' could not be found.")

# ==========================================
# 2. ECONOMETRIC MODEL SPECIFICATION
# ==========================================
# Instantiating the model with the panel data structure.
model = ThresholdPanel(
    data=df, 
    dep='y',             # Dependent variable (Y)
    indep=['x1', 'x2'],  # Control variables (regime-independent)
    rx=['rx1'],          # Regime-dependent variable(s) (subject to structural break)
    qx='q',              # Endogenous threshold variable determining the transition
    entity_col='id',     # Cross-sectional identifier (e.g., countries, firms)
    time_col='year'      # Time-series identifier (e.g., years)
)

# ==========================================
# 3. MODEL ESTIMATION AND BOOTSTRAP
# ==========================================
# Executing the search engine and simulating the asymptotic distribution.
# 
# Parameters:
# - thnum=1   : Forces the estimation of a single threshold.
# - trim=0.05 : Trims 5% of observations at the extremes to ensure 
#               matrix invertibility within each regime.
# - grid=0    : Perfect exhaustive search over exact values 
#               (eliminates the grid interpolation error found in legacy software).
# - bs=300    : 300 replications for the residual bootstrap (computes P-values).
model.fit(thnum=1, trim=0.05, grid=0, bs=300)

# ==========================================
# 4. INFERENCE AND RESULTS
# ==========================================
# Display the full regression results table in standard academic format.
model.summary()

See examples/example.py

Performance

Because non-dynamic threshold modeling relies on intensive grid searches and massive residual-based bootstrapping, computational speed is paramount. pyxthreg solves this via a hybrid Python/Numba architecture: an analytic incremental search that avoids rebuilding the design matrix at every grid point, on top of JIT compilation and multi-core bootstrap parallelization.

Benchmarked against a live, licensed Stata 17 run of the exact reference specification from Wang (2015) on the original Hansen (1999) dataset ($N=565$, $T=14$, grid=400, trim=0.01, bs=300): pyxthreg completes a warm run in 1.03s (median of 5 timed runs), versus 57.4s for Stata on the same machine (median of 3 timed runs) — roughly 56x faster, with point estimates, standard errors, $R^2$, and the true $F$-statistic matching Stata to 4–6 significant figures. This is a dated, scripted, reproducible re-run (3 August 2026); see documentation/wp-user-guide/main.pdf (§ Conformity with Stata, § Performance) for the full numeric comparison and documentation/wp-methodology/main.pdf for the complete derivation of every optimization. An earlier, unverified claim of "~4x speedup vs. 125s in Stata on 20,000 observations" could not be reproduced against a real Stata run and has been retired in favor of the measurements above.

📚 Documentation

All companion documents are posted as Working Papers (personal template, ready for SSRN) with versioned LaTeX sources alongside each PDF:

• documentation/wp-user-guide/main.pdf — complete practical reference: installation, every .fit() parameter, the full results dictionary, output interpretation, plotting, LaTeX/Stargazer export, worked examples on the bundled datasets, troubleshooting, and the Stata conformity table.
• documentation/wp-methodology/main.pdf — complete econometric and algebraic derivation: the fixed-effects model, the within-transformation projection algebra, Hansen's sequential search and refinement, the residual bootstrap theory, standard-error derivations, the LR-inversion confidence intervals, and full proofs behind the fast incremental search engine.

📖 References & Methodology

This package implements the algorithms and corrections outlined in the following seminal papers:

Hansen, B. E. (1999). Threshold effects in non-dynamic panels: Estimation, testing, and inference. Journal of Econometrics, 93(2), 345-368.

Hansen, B. E. (2000). Sample splitting and threshold estimation. Econometrica, 68(3), 575-603.

Davies, R. B. (1977). Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika, 64(2), 247-254.

Wang, Q. (2015). Fixed-effect panel threshold model using Stata. The Stata Journal, 15(1), 121-131.

🤝 Contributing

Contributions, issues, and feature requests are highly welcome! Because this package utilizes Numba JIT compilation, please ensure that any modifications to the core engine (core.py, sequential.py, bootstrap.py, inference.py) strictly adhere to @njit/nopython constraints, and that pytest tests/ (including the golden-master regression suite) still passes. Feel free to check the issues page on the GitHub repository.

License

MIT License. See LICENSE if included in the distribution.