Arco: an artificial counterfactual approach for high-dimensional panel time-series data

We consider a new, flexible and easy-to-implement method to estimate causal effects of an intervention on a single treated unit and when a control group is not readily available. We propose a two-step methodology where in the first stage a counterfactual is estimated from a large-dimensional set of variables from a pool of untreated units using shrinkage methods, such as the Least Absolute Shrinkage Operator (LASSO). In the second stage, we estimate the average intervention effect on a vector of variables, which is consistent and asymptotically normal. Our results are valid uniformly over a wide class of probability laws. Furthermore, we show that these results still hold when the exact date of the intervention is unknown. Tests for multiple interventions and for contamination effects are also derived. By a simple transformation of the variables of interest, it is also possible to test for intervention effects on several moments (such as the mean or the variance) of the variables of interest. A Monte Carlo experiment evaluates the properties of the method in finite samples and compares it with other alternatives such as the differences-in-differences, factor and the synthetic control methods. In an application we evaluate the effects on inflation of an anti tax evasion program.