ArCo: An artificial counterfactual approach for high-dimensional panel time-series data

Abstract

We consider a new, flexible and easy-to-implement method to estimate thecausal effects of an intervention on a single treated unit when a control group is not available and which nests previous proposals in the literature. It is a two-step methodology where in the first stage, a counterfactual is estimated based on a large-dimensional set of variables from a pool of untreated units by means of shrinkage methods, such as the least absolute shrinkage and selection 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. We show that these results hold even when the exact date of the intervention is unknown. Tests for multiple interventions and for contamination effects are derived. By a simple transformation of the variables, it is possible to test for multivariate intervention effects on several moments of the variables of interest. Existing methods in the literature usually test for intervention effects on a single variable and assume that the time of the intervention is known. In addition, high-dimensionality is frequently ignored and inference is either conducted under a set of more stringent hypotheses and/or by permutation tests. A Monte Carlo experiment evaluates the properties of the method in finite samples and compares it with other alternatives. As an application, we evaluate the effects on inflation, GDP growth, retail sales and credit of an anti tax-evasion program.