On Proximal Causal Inference With Synthetic Controls
Year: 2021
Type: preprint
Abstract: We aim to evaluate the causal impact of an intervention when time series data on a single treated unit and multiple untreated units are available, in pre- and post- treatment periods. In their seminal work, Abadie and Gardeazabal (2003) and Abadie et al. (2010) proposed a (SC) method as an approach to relax the parallel trend assumption on which difference-in-differences methods typically rely upon. The term synthetic control refers to a weighted average of units built to match the treated unit's pre-treatment outcome trajectory, such that the SC's post-treatment outcome predicts the treated unit's unobserved potential outcome under no treatment. The treatment effect is then estimated as the difference in post-treatment outcomes between the treated unit and the SC. A common practice to estimate the weights is to regress the pre-treatment outcome process of the treated unit on that of units using ordinary or weighted (constrained) least squares. However, it has been established that these estimators can fail to be consistent under standard time series asymptotic regimes. Furthermore, inferences with controls are typically performed by placebo test which lacks formal justification. In this paper, we introduce a proximal causal inference framework for the approach and formalize identification and inference for both the weights and the treatment effect on the treated unit. We further extend the traditional linear interactive fixed effects model to accommodate more general nonlinear models allowing for binary and count outcomes which are currently under-studied in the literature. We illustrate our proposed methods with simulation studies and an application to the evaluation of the 1990 German Reunification.
Source: arXiv (Cornell University)
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3197317602