A robust regression approach to synthetic control with interference

Thomas M. Menino Convention & Exhibition Center 

Synthetic control methods are widely used for policy evaluation, but most existing methods rule out interference among units, compromising validity when such effects are present.
We develop a framework that accommodates contaminated donor pools and unknown interference patterns through two stages: factor-model adjustment for unobserved confounding, followed by robust regression in which direct and interference effects appear as a sparse outlier component.
When the number of units is fixed and at least half are unaffected by interference, high-breakdown robust regression yields consistent identification of valid controls and asymptotically normal inference. When the number of units diverges, we allow for sparse large and dense weak interference, with robust M-estimation remaining valid even when the post-intervention period is short.
Unlike methods requiring pre-specified valid controls or parametric modeling of interference, our framework relies only on coarse sparsity information and enables formal inference on both direct and interference effects.
Simulations and two empirical examples demonstrate the method's validity and reveal novel insights about interference effects.

comparative case study

factor analysis

policy evaluation

interference effect

robust regression 

Business and Economic Statistics Section