Synthetic control methods are used for conducting causal inference with longitudinal data. Their popularity comes from the intuitive interpretation of their results, as well as their ability to estimate causal effects on a single treated unit.
These methods work by creating a synthetic unit (city/region/country/etc) that is as similar as possible to the one that has received some sort of intervention (the so-called 'treated' unit), or where a policy has been adopted, except for the intervention/policy itself. Any difference between the real unit and the synthetic one on the outcome of interest is deemed to have been caused by the policy or intervention.
In recent years, there has been an explosion of expansions to synthetic control methods, allowing not only single-case studies but also small, medium, and large-N analysis and inference.
The first session starts with the potential outcomes framework (or Rubin Causal Model), which underlies the synthetic controls framework. We discuss the foundations of how and when the estimates of synthetic controls can be causally identified, and introduce the notation used in the course.
We follow with a conceptual discussion on assumptions, applicability, estimation, and inference. We discuss how the weights are assigned, data requirements for estimation, and how to interpret results.
We end this first day with a practical session on implementing synthetic controls. Examples will be given in R, but Stata code will be provided for those who prefer it.
We start with robustness and sensitivity tests, namely placebo tests which are used for inference and testing assumptions. We cover placebo-in-time tests, as well as the construction of placebos for significance testing. We also look at sensitivity tests, such as the jackknife, to assess how robust the results are in relation to the untreated units in the sample.
We then move to applications of synthetic controls to multiple treated units, an emerging area in this topic. This session covers how to build synthetic controls for several units, how to assess the fit of controls, calculate an average treatment effect, and bootstrapping methods for testing the significance of results.
After a lab practice, we go to recent advanced applications of synthetic controls, and look at generalised synthetic control models.
By the end of this course you will be able to identify the proper specifications of synthetic controls for your data, how to implement these models and rigorously test their assumptions to make inferences.