How to Make Causal Inferences with Time-Series Cross-Sectional Data under Selection on Observables
by Matthew Blackwell, Harvard University and Adam N. Glynn, Emory University
Repeated measurements of the same countries, people, or groups over time are vital to manyfields of political science. These measurements, sometimes called timeseries crosssectional TSCS) data, allow researchers to estimate a broad set of causal quantities, including contemporaneous effects and direct effects of lagged treatments. Unfortunately, popular methods for TSCS data can only produce valid inferences for lagged effects under very strong assumptions. In this paper, we use potential outcomes to define causal quantities of interest in this settings and clarify how standard models like the autoregressive distributed lag model can produce biased estimates of these quantities due to posttreatment conditioning even when a selection on observables assumption holds. We then describe two estimation strategies that avoid these posttreatment biasesinverse probability weighting and structural nested mean modelsand show via simulations that they can outperform standard approaches in small sample settings. We illustrate these methods in a study of how welfare spending affects terrorism.