Causal Inference in Python

Chapter 9. Synthetic Control

In the previous chapter you learned about the advantages of panel data for causal identification. Namely, the fact that you could not only compare units with each other, but also with their former selves, allows you to estimate counterfactuals $Y_0$ with more plausible assumptions. You also learned about difference-in-differences (DID)—and many variations of it—one of the many causal inference tools that leverage panel data. By relying on similar (parallel) growth trajectories between treated and control, DID was able to identify the treatment effect even if the levels of $Y_0$ between treated and control were different. In this chapter, you’ll learn another popular technique for panel datasets: synthetic control (SC).

While DID works great if you have a relatively large number of units $N$ compared to time periods $T$, it falls short when the reverse is true. In contrast, synthetic control was designed to work with very few, even one, treatment unit. The idea behind it is quite simple: combine the control units in order to craft a synthetic control that would approximate the behavior of the treated units in the absence of treatment. By doing that, it avoids making a parallel trend assumption as the synthetic control, when well crafted, won’t be just parallel, but perfectly overlapping with the counterfactual $E\left[Y_0\right|D=1]$.

At the end of this chapter, you’ll also learn how to combine both DID and SC. This combined estimator is not only ...