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 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-indifferences , factor and the synthetic control methods. In an application we evaluate the effects on inflation of an anti tax evasion program.

Assessing the Causal Effect of Binary Interventions from Observational Panel Data with Few Treated Units

“…The SCM, HCW, DI and CIM assume a linear relationship between the outcome of the treated unit and the outcomes of control units but this is a strong assumption. Carvalho, Masini and Medeiros (2018) account for non-linear relationships by regressing y n1+1,t on transformations of the outcomes of control units but it is hard to choose which transformations to use. Therefore, it would be worth estimating the relationship between y n1+1,t and the outcomes of the control units non-parametrically using, for example, machine learning techniques.…”

Large Dimensional Latent Factor Modeling with Missing Observations and Applications to Causal Inference

“…A popular model assumption is that the potential outcome is linear in observed covariates and unobserved common factors (Abadie et al, 2010(Abadie et al, , 2015. Abadie et al (2010Abadie et al ( , 2015, Hsiao et al (2012), Doudchenko and Imbens (2016), Li and Bell (2017), Li (2017), Carvalho et al (2018), andMasini andMedeiros (2018) propose to match each treated unit by weighted averages of all control units using the pretreatment observations. Li and Bell (2017) and Li (2017) further show the inferential theory for the average treatment effect over time.…”

“…using the LASSO method to select control units and Carvalho et al (2018) show the inferential theory for the LASSO method. Masini and Medeiros (2018) focus on the high-dimensional, nonstationary data.…”

Non-Conventional Monetary Policy in Turkey: A Synthetic Control Approach

“…The goal is to estimate how the outcome variables would have behaved had Turkey not implemented the new set of instruments. In addition, we construct another artificial counterfactual using the method proposed by Carvalho et al (2016). Previous works explored the impact of macro-prudential policies on central bank efficiency.…”

“…In the synthetic control method, we construct a comparison unit by attributing different weights to available control countries, based on the preintervention period. The artificial counterfactual suggested by Carvalho et al (2016) is arguably similar and it works in a two-step approach: the first is estimating a model using the data previous to the event of interest, and the second is estimating the average intervention effect on the treated unit. Their model allows for multiple variables analysis, as well as a defined inference procedure.…”