Matching Methods for Causal Inference with Time‐Series Cross‐Sectional Data

Abstract

Matching methods improve the validity of causal inference by reducing model dependence and offering intuitive diagnostics. Although they have become a part of the standard tool kit across disciplines, matching methods are rarely used when analysing time-series cross-sectional data. We fill this methodological gap. In the proposed approach, we first match each treated observation with control observations from other units in the same time period that have an identical treatment history up to the prespecified number of lags. We use standard matching and weighting methods to further refine this matched set so that the treated and matched control observations have similar covariate values. Assessing the quality of matches is done by examining covariate balance. Finally, we estimate both short-term and long-term average treatment effects using the difference-in-differences estimator, accounting for a time trend. We illustrate the proposed methodology through simulation and empirical studies. An open-source software package is available for implementing the proposed methods.

A Practical Guide to Counterfactual Estimators for Causal Inference with Time-Series Cross-Sectional Data

“…Our methods have several limitations. First, the strict exogeneity assumption, which corresponds to within-unit randomization, may be unrealistic in many applied settings, in which case researchers should consider methods based on sequential ignorability (Blackwell and Glynn 2018;Imai, Kim and Wang 2018;Hazlett and Xu 2018). Second, although we provide flexible modeling options, such as IFEct and MC, they are no panacea for all TSCS applications.…”

Synthetic learner: model-free inference on treatments over time

“…With a slight abuse of notation, we consider potential outcomes of the form Y t (d (t−m):t ). The noanticipation assumption has been previously discussed in Abbring and Heckman (2007), , while the restricted carryover effect is analogous to the identification assumption stated in Imai et al (2018), Iavor Bojinov (2019, Blackwell and Glynn (2018) among others. Carryover effects have not been considered in previous literature on Synthetic Control.…”

“…We generalize the notion of treatment effects for time-dependent data by allowing for carry-over effects, i.e., treatment assignment is possibly dependent on past treatment assignments. The framework rephrases causal estimands as a function of the entire treatment history and leans on the recent literature on treatments over time that include, among others, Iavor Bojinov (2019); Robins et al (2000); Blackwell and Glynn (2018); Hernán and Robins (2015); Abraham and Sun (2018); ; Imai et al (2018), while it brings substantial innovation in the definition of the causal estimands of interest with respect to the past literature on the Synthetic Control.…”

“…Inference for SC with linear, high-dimensional outcome model was recently developed by . Imai et al (2018) discusses bootstrap approximations following K-nearest neighbors and matching. However, formal inferential justifications were not further discussed therein.…”

Social Distancing and COVID-19: Randomization Inference for a Structured Dose-Response Relationship

“…According to Li et al (2001)'s setup, units receive a binary treatment at most once in the entire study period. Our framework is also different from Imai et al (2018). Imai et al (2018)'s primary interest is the treatment effect of an intervention at a particular time point t; hence, Imai et al…”