Benchmarking Structural Gravity Estimators: PPML vs. Polyads on Sparse Trade Data

Overview

This project benchmarks two structural gravity estimators—the industry-standard Pseudo-Poisson Maximum Likelihood (PPML) and the novel Polyad estimator (Resende, Lecué, Wilner & Choné, 2026)—on large-scale, sparse international trade data. The work was produced for the Statistical Modeling Seminar at ENSAE Paris (2026).

PPML is the standard workhorse of the trade gravity literature, valued for its robustness to heteroskedasticity and consistent handling of zero trade flows. However, it is subject to the Incidental Parameter Problem (IPP) and faces computational bottlenecks as network dimensionality grows. The Polyad estimator reformulates fixed-effects elimination as a classification task, offering theoretically unbiased estimates with valid confidence intervals under heavy sparsity—a setting where PPML is known to break down.

Research Question

Does the Polyad estimator deliver less-biased and better-calibrated estimates of Regional Trade Agreement (RTA) effects than PPML when applied to high-dimensional, sparse gravity networks?

Data

Source	Description
CEPII BACI	Bilateral trade flows at the HS-6 product level — provides a naturally high-dimensional, sparse bilateral trade matrix
CEPII Gravity Database	Country-pair covariates: geodesic distances, GDPs, contiguity, common language, and RTA membership dummies

Zero-flows are injected systematically into the BACI dataset to amplify sparsity and stress-test both estimators under conditions representative of real-world disaggregated trade networks.

Raw data files are not included due to size constraints. See data/README.md for download and placement instructions from the CEPII website.

Methodology

1. Data Engineering — Merge BACI trade flows with gravity covariates at the HS-6 level and inject zero-flows to construct a sparse bilateral trade matrix suitable for benchmarking.
2. PPML Benchmark — Estimate RTA effects using the fixest package in R, absorbing high-dimensional exporter × year and importer × year fixed effects via the Frisch–Waugh–Lovell theorem.
3. Polyad Estimation — Deploy the polyads Python library (Resende et al., 2026) to eliminate fixed effects via a classification sub-problem and recover structural parameters under sparsity.
4. Evaluation — Compare point estimates, standard errors, and confidence interval coverage across both estimators at varying sparsity levels.

Stack: Python 3.10+ (polyads, pandas, numpy, scikit-learn) · R (fixest, data.table)

Key Results

Estimator	RTA Coefficient	95% CI Coverage	Notes
PPML (fixest)	—	—	High-dimensional FE benchmark
Polyads	—	—	Classification-based FE elimination

Full coefficient tables and coverage plots will be available in results/ upon completion of the benchmarking pipeline.

Replication

# 1. Clone the repository
git clone https://github.com/VarnelT/estimator-Polyads-vs-PPML.git
cd estimator-Polyads-vs-PPML

# 2. Download CEPII BACI and Gravity data, place in data/raw/
#    Instructions: see data/README.md

# 3. Install Python dependencies
pip install pandas numpy scikit-learn matplotlib

# 4. Build the sparse gravity dataset (merge BACI + Gravity, inject zero-flows)
python src/01_build_dataset.py

# 5. Run the PPML benchmark (R)
Rscript src/02_benchmark_ppml.R

# 6. Run the Polyads estimation (Python)
python src/03_estimation_polyads.py

# 7. Generate the coefficient comparison plot
python src/04_plot_results.py

# 8. Generate the computational complexity table
python src/05_generate_complexity_table.py

Results are written to results/ as PNG coefficient plots and complexity tables.

References

• Resende, G., Lecué, G., Wilner, L., & Choné, P. (2026). Polyad Estimator for Large Multi-Way Networks. arXiv:2512.02203.
• Santos Silva, J. M. C., & Tenreyro, S. (2006). The Log of Gravity. The Review of Economics and Statistics, 88(4), 641–658.
• Bergé, L. (2018). Efficient estimation of maximum likelihood models with multiple fixed-effects. The Stata Journal, 18(4), 796–820.

---

Statistical Modeling Seminar — ENSAE Paris, 2026