Tactics for Design and Inference in Synthetic Control Studies: An Applied Example Using High-Dimensional Data

Abstract

We describe identification assumptions underlying synthetic control studies and offer recommendations for key-and normally ad hoc-implementation decisions, focusing on model selection; model fit; cross-validation; and decision rules for inference. We outline how to implement a Synthetic Control Using Lasso (SCUL). The method-available as an R packageallows for a high-dimensional donor pool; automates model selection; includes donors from a wide range of variable types; and permits both extrapolation and negative weights. In an application, we employ our recommendations and the SCUL strategy to estimate how recreational marijuana legalization affects sales of alcohol and over-the-counter painkillers, finding reductions in alcohol sales.

Front-of-Pack Labeling in Chile: Effects on Employment, Real Wages, and Firms’ Profits after Three Years of Its Implementation

“…Hence, if after the first intervention levels and trends of the synthetic group are changed with respect to the treated group, such changes can be attributed to the intervention [19]. Because there is not a single class of economic activity capable of replicating the pre-intervention behavior of the treated group, the synthetic group is constructed using several "donors" (i.e., classes of economic activities not affected by the interventions) that are weighted using the SCUL (Synthetic Control Using Lasso) methodology [20]. As the name suggests, it applies lasso regressions, which are "penalized Ordinary Least Square (OLS)" to prevent the over-adjustment that a regular OLS would have in the usual presence of autocorrelation in time series, which would lead to inadequate predictions off-sample [20].…”

“…As the name suggests, it applies lasso regressions, which are "penalized Ordinary Least Square (OLS)" to prevent the over-adjustment that a regular OLS would have in the usual presence of autocorrelation in time series, which would lead to inadequate predictions off-sample [20]. Details of the methodology and a package in R for its application are available elsewhere [20].…”

Just Do IT? An Assessment of Inflation Targeting in a Global Comparative Case Study

“…Table 4 reports measures of pre-treatment fit. We show the values of the root mean squared prediction error (RMSPE), mean absolute prediction error (MAPE), the standard deviation (SD), and the MAPE rescaled by the SD (Hollingsworth and Wing, 2020), all calculated over the preintervention period. We constrain our analysis to all the units with RMSPE lower than 3 p.p.…”

“…It is important to note that a (very) good pre-intervention fit is a necessary but not a sufficient condition for a proper SC estimation due to the risk of over-fitting (seeAbadie and Vives-i-Bastida, 2022).28 To the best of our knowledge, the literature on the SC method does not propose an optimal procedure to determine what a "very good" pre-treatment fit is. Based on the propensity score matching literature,Hollingsworth and Wing (2020) recommend to ignore units with synthetic pre-intervention fit measured by the MAPE-to-SD ratio larger than 0.25. The authors, however, acknowledge that this threshold value is arbitrary.…”

Pursuing Environmental and Social Objectives through Trade Agreements

“…The constructed comparability that derives from the double-weighting procedure allows the SDID estimator to potentially compensate for a lack of parallel pre-trends between treated and untreated units in the raw data, an issue that might affect the robustness of traditional DID estimators. At the same time, becasue of the inclusion of two-way fixed effects and of a different weighting algorithm, it does not require an exact match of pre-treatment trends of treated and non-treated units, a rarely satisfied requirement of the synthetic control method (Hollingsworth and Wing, 2020;McClelland and Mucciolo, 2022).…”