Consistency of an Intercept-Shifted Synthetic-Control Estimator under Weighted Parallel Trends

TL;DR

This paper establishes the consistency of an intercept-shifted synthetic control estimator for treatment effects in staggered adoption settings, under weighted parallel trends and mild regularity conditions, even with heavy-tailed shocks.

Contribution

It introduces a new consistency result for an intercept-augmented synthetic control estimator under weighted parallel trends and expands the valid data generating process assumptions.

Findings

Consistency achieved under weighted parallel trends and regularity conditions.

Conditions are more interpretable than traditional autoregressive or low-rank models.

Practical diagnostics are discussed for validating assumptions.

Abstract

The average treatment effect on the treated (ATT) in a staggered-adoption panel is estimated using an intercept-augmented synthetic-control (SCM) estimator. A weighted parallel trends plus an intercept shift, together with mild regularity on the weight vectors (non-degenerate dispersion) and expanding pre-treatment length, are sufficient for consistency allowing for heavy-tailed shocks. These conditions can be more interpretable than the autoregressive or low-rank factor models with light tails assumed by Ben-Michael, Feller, and Rothstein (2022) and expand the valid DGP pool from the same paper. Practical diagnostics to support the assumptions are discussed and situate these results within the recent literature on SC + DiD hybrids.