Time-series cross-sectional (TSCS) data, featuring repeated observations of units over time, is common in political science research. This study addresses a critical limitation: standard methods for estimating lagged treatment effects often produce biased results when selection on observables occurs post-treatment. Using potential outcomes as the foundation, the paper demonstrates how popular models like autoregressive distributed lags can be flawed due to conditioning on post-outcome variables.

The authors propose two novel estimation strategies—inverse probability weighting and structural nested mean models—as alternatives that mitigate these biases. Through simulations, they show these approaches perform better than standard methods in small sample sizes.

To illustrate the practical application of their framework, we examine welfare spending's relationship with terrorism. The findings highlight how careful methodological choices are essential for accurate causal inference when analyzing dynamic political phenomena.