Published online by Cambridge University Press: 03 August 2018
Repeated measurements of the same countries, people, or groups over time are vital to many fields of political science. These measurements, sometimes called time-series cross-sectional (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 some strong assumptions. In this paper, we use potential outcomes to define causal quantities of interest in these settings and clarify how standard models like the autoregressive distributed lag model can produce biased estimates of these quantities due to post-treatment conditioning. We then describe two estimation strategies that avoid these post-treatment biases—inverse probability weighting and structural nested mean models—and 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.
We are grateful to Neal Beck, Jake Bowers, Patrick Brandt, Simo Goshev, and Cyrus Samii for helpful advice and feedback and Elisha Cohen for research support. Any remaining errors are our own. This research project was supported by Riksbankens Jubileumsfond, Grant M13-0559:1, PI: Staffan I. Lindberg, V-Dem Institute, University of Gothenburg, Sweden and by European Research Council, Grant 724191, PI: Staffan I. Lindberg, V-Dem Institute, University of Gothenburg, Sweden. Replication files are available on the American Political Science Review Dataverse: https://doi.org/10.7910/DVN/SFBX6Z.
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