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

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractWe 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.

ArCo: An R package to Estimate Artificial Counterfactuals

“…This can happen either when the number of peers and/or the number of variables for each peer is large or when the sample size is too small. In Carvalho et al (2016b) the authors consider a linear model estimated by the Least Absolute Selection and Shrinkage Operator (LASSO) proposed by Tibshirani (1996). However, in the R package we leave the choice of the conditioning model to the user.…”

“…LASSO regressions (and extensions), regression trees and random forests, boosted trees, neural networks, splines, factor models, are some possible examples of models to be estimated in the first step. The results in Carvalho et al (2016b) are derived under asymptotic limits on the time dimension (T). However, the authors allow the number of peers (n) and the number of observed variables for each peer to grow as a function of T.…”

“…This section aims to describe the mathematical notation and the key definitions of the ArCo methodology in a way that is compatible with the ArCo (Fonseca et al, 2017) package. For further details on statistical properties and theoretical results, see Carvalho et al (2016b) and Carvalho et al (2016a). Everything concerning the technique used to estimate the first-step model is left in a very general way as the ArCo package was developed to accept many different classes of models.…”

An exact and robust conformal inference method for counterfactual and synthetic controls

“…Asymptotic approaches often focus on testing hypotheses about average effect over time,ᾱ, and require that T 0 and often also T * tend to infinity. Carvalho et al (2017) derive the asymptotic distribution ofᾱ in setups where the counterfactual is estimated based on Lasso and Li (2017) studies inference based on the constrained least squares estimator of Abadie et al (2010Abadie et al ( , 2015. Xu (2017) proposes an asymptotic bootstrap inference procedure based on factor models, but leaves the formal justification of this procedure for future research.…”

“…In addition to testing sharp null hypotheses, researchers are often also interested in testing hypotheses about average effects (e.g., Gobillon and Magnac, 2016;Carvalho et al, 2017;Li, 2017):…”