Simple Difference-in-Differences Estimation in Fixed-T Panels

Nicholas Brown¹, Kyle Butts², and Joakim Westerlund^3,4
1Queen's University, ²University of Colorado: Boulder, ³Lund University, ⁴Deakin University

Paper

Abstract

The present paper proposes a new treatment effects estimator that is valid when the number of time periods is small, and the parallel trends condition holds conditional on covariates and unobserved heterogeneity in the form of interactive fixed effects. The estimator also allow the control variables to be affected by treatment and it enables estimation of the resulting indirect effect on the outcome variable. The asymptotic properties of the estimator are established and their accuracy in small samples is investigated using Monte Carlo simulations. The empirical usefulness of the estimator is illustrated using as an example the effect of increased trade competition on firm markups in China.

Replication

Monte Carlo Simulations

1. code/simulations/simulation-1.jl

• Simulations presented in Table 1 and Table 2
• There are set of helper functions in code/simulations/helpers.module.jl containing estimation functions and the DGP.

Application

1. code/Trade-Liberalization-and-Markup-Dispersion/analysis.R

• Takes the data from Lu and Yu (2015) and recreates Figure 2 in their paper.
• Estimates the C²ED² model to estimate the effect of TWO ascension on markup dispersion in high-tariff industries.
• Decomposes the effect into the mediated effect via decrease in marginal cost dispersion.

Citation

@article{brown2023difference,
  title={Difference-in-Differences via Common Correlated Effects},
  author={Brown, Nicholas and Butts, Kyle and Westerlund, Joakim},
  journal={arXiv preprint arXiv:2301.11358},
  year={2023}
}