Probably because of their interpretability and transparent nature, synthetic controls have become widely applied in empirical research in economics and the social sciences. This article aims to provide practical guidance to researchers employing synthetic control methods. The article starts with an overview and an introduction to synthetic control estimation. The main sections discuss the advantages of the synthetic control framework as a research design, and describe the settings where synthetic controls provide reliable estimates and those where they may fail. The article closes with a discussion of recent extensions, related methods, and avenues for future research.

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This article provides an empirical investigation of the determinants of terrorism at the country level. In contrast with the previous literature on this subject, which focuses on transnational terrorism only, I use a new measure of terrorism that encompasses both domestic and transnational terrorism. In line with the results of some recent studies, this article shows that terrorist risk is not significantly higher for poorer countries, once the effects of other country-specific characteristics such as the level of political freedom are taken into account. Political freedom is shown to explain terrorism, but it does so in a non-monotonic way: countries in some intermediate range of political freedom are shown to be more prone to terrorism than countries with high levels of political freedom or countries with highly authoritarian regimes. This result suggests that, as experienced recently in Iraq and previously in Spain and Russia, transitions from an authoritarian regime to a democracy may be accompanied by temporary increases in terrorism. Finally, the results suggest that geographic factors are important to sustain terrorist activities.

This article investigates the economic effects of conflict, using the terrorist conflict in the Basque Country as a case study. We find that, after the outbreak of terrorism in the late 1960's, per capita GDP in the Basque Country declined about 10 percentage points relative to a synthetic control region without terrorism. In addition, we use the 1998–1999 truce as a natural experiment. We find that stocks of firms with a significant part of their business in the Basque Country showed a positive relative performance when truce became credible, and a negative relative performance at the end of the cease-fire.

This paper studies how to design experiments when the experimental units are large aggregate entities (e.g., markets), and only one or a small number of units can be treated. We propose a class of non-randomized experimental designs using the synthetic control method, which jointly selects treated units and untreated units to serve as a comparison group. We analyze the properties of estimators under these synthetic control designs and develop new inferential techniques. We show that, in experiments with aggregate units, synthetic control designs can substantially reduce estimation bias relative to randomized experiments.

Many settings in empirical economics involve estimation of a large number of parameters. In such settings, methods that combine regularized estimation and data-driven choices of regularization parameters are useful. We provide guidance to applied researchers on the choice between regularized estimators and data-driven selection of regularization parameters. We characterize the risk and relative performance of regularized estimators as a function of the data-generating process and show that data-driven choices of regularization parameters yield estimators with risk uniformly close to the risk attained under the optimal (unfeasible) choice of regularization parameters. We illustrate using examples from empirical economics.

Policymakers are often interested in estimating how policy interventions affect the outcomes of those most in need of help. This concern has motivated the practice of disaggregating experimental results by groups constructed on the basis of an index of baseline characteristics that predicts the values of individual outcomes without the treatment. This paper shows that substantial biases may arise in practice if the index is estimated by regressing the outcome variable on baseline characteristics for the full sample of experimental controls. We propose alternative methods that correct this bias and show that they behave well in realistic scenarios.

Propensity score matching estimators (Rosenbaum and Rubin (1983)) are widely used in evaluation research to estimate average treatment effects. In this article, we derive the large sample distribution of propensity score matching estimators. Our derivations take into account that the propensity score is itself estimated in a first step, prior to matching. We prove that first step estimation of the propensity score affects the large sample distribution of propensity score matching estimators, and derive adjustments to the large sample variances of propensity score matching estimators of the average treatment effect (ATE) and the average treatment effect on the treated (ATET). The adjustment for the ATE estimator is negative (or zero in some special cases), implying that matching on the estimated propensity score is more efficient than matching on the true propensity score in large samples. However, for the ATET estimator, the sign of the adjustment term depends on the data generating process, and ignoring the estimation error in the propensity score may lead to confidence intervals that are either too large or too small.

Matching estimators are widely used in empirical economics for the evaluation of programs or treatments. Researchers using matching methods often apply the bootstrap to calculate the standard errors. However, no formal justification has been provided for the use of the bootstrap in this setting. In this article, we show that the standard bootstrap is, in general, not valid for matching estimators, even in the simple case with a single continuous covariate where the estimator is root-N consistent and asymptotically normally distributed with zero asymptotic bias. Valid inferential methods in this setting are the analytic asymptotic variance estimator of Abadie and Imbens (2006a) as well as certain modifications of the standard bootstrap, like the subsampling methods in Politis and Romano (1994).

Matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases. The absence of formal results in this area may be partly due to the fact that standard asymptotic expansions do not apply to matching estimators with a fixed number of matches because such estimators are highly nonsmooth functionals of the data. In this article we develop new methods for analyzing the large sample properties of matching estimators and establish a number of new results. We focus on matching with replacement with a fixed number of matches. First, we show that matching estimators are not N1/2-consistent in general and describe conditions under which matching estimators do attain N1/2-consistency. Second, we show that even in settings where matching estimators are N1/2-consistent, simple matching estimators with a fixed number of matches do not attain the semiparametric efficiency bound. Third, we provide a consistent estimator for the large sample variance that does not require consistent nonparametric estimation of unknown functions. Software for implementing these methods is available in Matlab, Stata, and R.