A primary challenge for researchers that make use of observational data is selection bias (i.e. the units of analysis exhibit systematic differences and dis-homogeneities due to non-random selection into treatment). This article encourages researchers in acknowledging this problem and discusses how and – more importantly – under which assumptions they may resort to statistical matching techniques to reduce the imbalance in the empirical distribution of pre-treatment observable variables between the treatment and control groups. With the aim of providing a practical guidance, the article engages with the evaluation of the effectiveness of peacekeeping missions in the case of the Bosnian civil war, a research topic in which selection bias is a structural feature of the observational data researchers have to use, and shows how to apply the Coarsened Exact Matching (CEM), the most widely used matching algorithm in the fields of Political Science and International Relations.

There is a long tradition of imputation studies looking at how abstainers would vote if they had to. This is crucial for democracies because when abstainers and voters have different preferences, the electoral outcome ceases to reflect the will of the people. In this paper, we apply a non-parametric method to revisit old evidence. We impute the vote of abstainers in 15 European countries using Coarsened Exact Matching (CEM). While traditional imputation methods rely on the choice of voters that are on average like abstainers, and simulate full turnout, CEM only imputes the vote of the abstainers that are similar to voters, and allows to simulate an electoral outcome under varying levels of turnout, including levels that credibly simulate compulsory voting. We find that higher turnout would benefit social democratic parties while imposing substantial losses to extreme left and green parties.

We show that propensity score matching (PSM), an enormously popular method of preprocessing data for causal inference, often accomplishes the opposite of its intended goal—thus increasing imbalance, inefficiency, model dependence, and bias. The weakness of PSM comes from its attempts to approximate a completely randomized experiment, rather than, as with other matching methods, a more efficient fully blocked randomized experiment. PSM is thus uniquely blind to the often large portion of imbalance that can be eliminated by approximating full blocking with other matching methods. Moreover, in data balanced enough to approximate complete randomization, either to begin with or after pruning some observations, PSM approximates random matching which, we show, increases imbalance even relative to the original data. Although these results suggest researchers replace PSM with one of the other available matching methods, propensity scores have other productive uses.