APPMLHDFE

The Tails of Gravity

The Tails of Gravity: Using Expectiles to Quantify the Trade-Margins Effects of Economic Integration Agreements

Github repository

Authors

• Jeffrey H. Bergstrand
• Matthew W. Clance
• J.M.C. Santos Silva

Overview

This repository introduces and implements the Poisson-based expectile regressions described in the article “The Tails of Gravity: Using Expectiles to Quantify the Trade-Margins Effects of Economic Integration Agreements”. The estimation method is called asymmetric Poisson pseudo maximum likelihood (APPML) estimation and is used to analyze heterogeneous effects in international trade, but it is also useful in many other applications.

The R script (appml_r2) has been adapted from the existing Stata command appmlhdfe.ado.

Stata:
Matthew Clance & J.M.C. Santos Silva, 2025. “APPMLHDFE: Stata module to estimate asymmetric Poisson regression with high-dimensional fixed effects,” Statistical Software Components S459414, Boston College Department of Economics.

Data:
Bergstrand, Jeffrey; Clance, Matthew; Santos Silva, Joao (2025), “The Tails of Gravity”, Mendeley Data, V1, doi: 10.17632/n67gft8fvm.1

What Are Expectile Regressions?

Expectile regressions extend the flexibility of traditional regression models by estimating effects across the entire conditional distribution of a dependent variable. Unlike quantile regressions, expectiles are global measures of location, providing robust insights into how covariates influence not just the mean but also the tails of the distribution.

Why Poisson-Based Expectiles?

The Poisson-based expectile regression approach combines the advantages of Poisson pseudo-maximum likelihood (PPML) with the ability to model heterogeneity across the distribution:

• Handles non-negative dependent variables (e.g., trade flows) with many zeros.
• Allows for high-dimensional panel data.
• Yields easily interpretable elasticities or semi-elasticities across different conditional expectiles.

Key Features

• Accommodates zeros: Unlike quantile regression, which struggles with mass points at zero, Poisson-based expectiles maintain smooth functional relationships.
• Heterogeneous effects: Captures how relationships vary across different parts of the distribution, from lower to upper tails.
• Easy implementation: Simple extensions of PPML make expectile estimation computationally efficient.

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Repository Contents

• R Scripts:
  • appml_r2.R: Function to estimate APPML is essentially a wrapper program using the fixest package’s feglm function. Note that you can estimate either a single expectile or multiple expectiles. When estimating multiple expectiles, using starting values from sequential (previous) estimates will speed up the process.
  • estimation_r2.R: Replicates Figure 1 and Table 4 in “The Tails of Gravity: Using Expectiles to Quantify the Trade-Margins Effects of Economic Integration Agreements”.
  • Sim_Chi2_updated.R: Replicates the small simulation in “The Tails of Gravity: Using Expectiles to Quantify the Trade-Margins Effects of Economic Integration Agreements”.
  • example/: Example of APPML using a simulated dataset.