ARCO: An Artificial Counterfactual Approach For High-Dimensional Panel Time-Series Data

Abstract

We consider a new method to estimate causal effects when a treated unit suffers a shock or an intervention, such as a policy change, but there is not a readily available control group or counterfactual. We propose a two-step approach where in the first stage an artificial counterfactual is estimated from a large-dimensional set of variables from pool of untreated units (donors pool) 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 belonging to the treated unit, 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 date of the intervention is unknown and must be estimated from the data. 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. Finally, we can disentangle the actual intervention effects from confounding factors that usually bias before-and-after estimators. A detailed Monte Carlo experiment evaluates the properties of the method in finite samples and compares our proposal with other alternatives such as the differences-in-differences, factor models and the synthetic control method. An empirical application to evaluate the effects on inflation of a new anti tax evasion program in Brazil is considered. Our methodology is inspired by different branches of the literature such as: the Synthetic Control method, the Global Vector Autoregressive models, the econometrics of structural breaks, and the counterfactual analysis based on macro-econometric and panel data models.