# Synthetic Controls Date: 2022-08-15 >[!abstract] What sort of quesitons can **Synthetic Control** allow us to answer? >- Questions that have to do with policy? >- What was the economic cost to West Germany of reunifications? >- What is the effect of high cigarette tax on smoking? >- What is the effect of right-to-work law on employment? > > To answer these kinds of questions, we need to know **what would have happened without the policy intervention.** Synthetic Controls does this by **creating an artificial version of the polity in question and comparing actual outcomes to the outcomes predicted by this esitimated synthetic control.** >[!TLDR] >**Across time instead of across units** ### AB Testing > It is now widely accepted that the gold standard technique to compute the **causal effect** of a treatment (a drug, ad, product, …) on an outcome of interest (a disease, firm revenue, customer satisfaction, …) is **AB testing**, a.k.a. randomized experiments. We randomly split a set of subjects (patients, users, customers, …) into a treatment and a control group and give the treatment to the treatment group. This procedure ensures that ex-ante, the only expected difference between the two groups is caused by the treatment. An underlying assumption when it comes to AB testing is that there is no **contamination** between the treatment and control group. > Giving a drug to one patient in the treatment group does not affect the health of patients in the control group. This might not be the case for example if we are trying to cure a contagious disease and the two groups are not isolated. The scenario above is an example of [[Network Effects]]. Here is where the idea of **Synthetic Control** comes in. >[!Synthetic Control] >The idea of synthetic control is to exploit the temporal variation in the data instead of the cross-sectional one (across time instead of across units). This method is extremely popular in the industry — e.g. in companies like [Google](https://proceedings.neurips.cc/paper/2021/file/48d23e87eb98cc2227b5a8c33fa00680-Paper.pdf), [Uber](https://eng.uber.com/causal-inference-at-uber/), [Facebook](https://research.facebook.com/publications/regression-adjustment-with-synthetic-controls-in-online-experiments/), [Microsoft](https://github.com/Microsoft/SparseSC), and [Amazon](https://www.amazon.science/publications/a-self-supervised-approach-to-hierarchical-forecasting-with-applications-to-groupwise-synthetic-controls) — because it is easy to interpret and deals with a setting that emerges often at large scales. > Synthetic control allows us to do causal inference when we have **as few as one treated unit** and **many control units** and we observe them **over time**. The idea is simple: combine untreated units so that they mimic the behavior of the treated unit as closely as possible, without the treatment. Then use this “synthetic unit” as a control. The method was first introduced by [Abadie, Diamond, and Hainmueller (2010)](https://www.tandfonline.com/doi/abs/10.1198/jasa.2009.ap08746) and has been called [“the most important innovation in the policy evaluation literature in the last few years”](https://www.aeaweb.org/articles?id=10.1257/jep.31.2.3). Moreover, it is widely used in the industry because of its simplicity and interpretability. >[!important] >The problem is that, as usual, we do not observe the counterfactual outcome for treated units, i.e. we do not know what would have happened to them if they had not been treated. This is known as the **fundamental problem of causal inference**. We could, of course, use the event study approach and compare pre- and post-treatment periods. Or even, compare year-over-year values. ## Continue HERE ## Sources - [Understanding Synthetic Control Methods](https://towardsdatascience.com/understanding-synthetic-control-methods-dd9a291885a1) (Medium Article) - [Synthetic Control](https://www.youtube.com/watch?v=1PQfeDT8zXM)(YouTube) - [SI 2021 Methods Lectures: Causal Inference Using Synthetic Controls&Regression Discontinuity Designs](https://www.youtube.com/watch?v=T2p9Wg650bY) (YouTube)