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In recent years, there has been a burst of innovative work on methods for estimating causal effects using observational data. Much of this work has extended and brought a renewed focus on old approaches such as matching, which is the focus of this review. The new developments highlight an old tension in the social sciences: a focus on research design versus a focus on quantitative models. This realization, along with the renewed interest in field experiments, has marked the return of foundational questions as opposed to a fascination with the latest estimator. I use studies of get-out-the-vote interventions to exemplify this development. Without an experiment, natural experiment, a discontinuity, or some other strong design, no amount of econometric or statistical modeling can make the move from correlation to causation persuasive.

In recent years, there has been a burst of innovative work on methods for estimating causal effects using observational data. Much of this work has extended & brought a renewed focus on old approaches such as matching, which is the focus of this review. The new developments highlight an old tension in the social sciences: a focus on research design versus a focus on quantitative models. This realization, along with the renewed interest in field experiments, has marked the return of foundational questions as opposed to a fascination with the latest estimator. I use studies of get-out-the-vote interventions to exemplify this development. Without an experiment, natural experiment, a discontinuity, or some other strong design, no amount of econometric or statistical modeling can make the move from correlation to causation persuasive. Adapted from the source document.

In contrast to statistical methods, a number of case study methods -- collectively referred to as Mill's methods, used by generations of social science researchers -- only consider deterministic relationships. They do so to their detriment because heeding the basic lessons of statistical inference can prevent serious inferential errors. Of particular importance is the use of conditional probabilities to compare relevant counterfactuals. A prominent example of work using Mill's methods is Theda Skocpol's States and Social Revolutions. Barbara Geddes's widely assigned critique of Skocpol's claim of a causal relationship between foreign threat & social revolution is valid if this relationship is considered to be deterministic. If, however, we interpret Skocpol's hypothesized causal relationship to be probabilistic, Geddes's data support Skocpol's hypothesis. But Skocpol, unlike Geddes, failed to provide the data necessary to compare conditional probabilities. Also problematic for Skocpol is the fact that when one makes causal inferences, conditional probabilities are of interest only insofar as they provide information about relevant counterfactuals. 1 Table, 50 References. Adapted from the source document.

Natural experiments help to overcome some of the obstacles researchers face when making causal inferences in the social sciences. However, even when natural interventions are randomly assigned, some of the treatment–control comparisons made available by natural experiments may not be valid. We offer a framework for clarifying the issues involved, which are subtle and often overlooked. We illustrate our framework by examining four different natural experiments used in the literature. In each case, random assignment of the intervention is not sufficient to provide an unbiased estimate of the causal effect. Additional assumptions are required that are problematic. For some examples, we propose alternative research designs that avoid these conceptual difficulties.

Following David Lee's pioneering work, numerous scholars have applied the regression discontinuity (RD) design to popular elections. Contrary to the assumptions of RD, however, we show that bare winners and bare losers in U.S. House elections (1942–2008) differ markedly on pretreatment covariates. Bare winners possess largeex antefinancial, experience, and incumbency advantages over their opponents and are usually the candidates predicted to win byCongressional Quarterly's pre-election ratings. Covariate imbalance actually worsens in the closest House elections. National partisan tides help explain these patterns. Previous works have missed this imbalance because they rely excessively on model-based extrapolation. We present evidence suggesting that sorting in close House elections is due mainly to activities on or before Election Day rather than postelection recounts or other manipulation. The sorting is so strong that it is impossible to achieve covariate balance between matched treated and control observations, making covariate adjustment a dubious enterprise. Although RD is problematic for postwar House elections, this example does highlight the design's advantages over alternatives: RD's assumptions are clear and weaker than model-based alternatives, and their implications are empirically testable.

We look at conventional methods for removing endogeneity bias in regression models, including the linear model and the probit model. It is known that the usual Heckman two-step procedure should not be used in the probit model: from a theoretical perspective, it is unsatisfactory, and likelihood methods are superior. However, serious numerical problems occur when standard software packages try to maximize the biprobit likelihood function, even if the number of covariates is small. We draw conclusions for statistical practice. Finally, we prove the conditions under which parameters in the model are identifiable. The conditions for identification are delicate; we believe these results are new.