Standard sufficient conditions for identification in the regression discontinuity design are continuity of the conditional expectation of counterfactual outcomes in the running variable. These continuity assumptions may not be plausible if agents are able to manipulate the running variable. This paper develops a test of manipulation related to continuity of the running variable density function. The methodology is applied to popular elections to the House of Representatives, where sorting is neither expected nor found, and to roll-call voting in the House, where sorting is both expected and found. I thank two anonymous referees for comments, the editors for multiple suggestions that substantially improved the paper, Jack Porter, John DiNardo, and Serena Ng for discussion, Jonah Gelbach for computing improvements, and Ming-Yen Cheng One reason for the increasing popularity in economics of regression discontinuity applications is the perception that the identifying assumptions are quite weak. However, while some applications of the design can be highly persuasive, many are subject to the criticism that public knowledge of the treatment assignment rule may invalidate the continuity assumptions at the heart of identification.

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This paper presents the econometric approach to causal modeling. It is motivated by pol-icy problems. New causal parameters are defined and identified to address specific policy problems. Economists embrace a scientific approach to causality and model the preferences and choices of agents to infer subjective (agent) evaluations as well as objective outcomes. Anticipated and realized subjective and objective outcomes are distinguished. Models for simultaneous causality are developed. The paper contrasts the Neyman–Rubin model of causality with the econometric approach.

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While interest in social determinants of individual behavior has led to a rich theoretical literature and many efforts to measure these influences, a mature “social econometrics ” has yet to emerge. This chapter provides a critical overview of the identification of social interactions. We consider linear and discrete choice models as well as social networks structures. We also consider experimental and quasi-experimental methods. In addition to describing the state of the identification literature, we indicate areas where additional research is especially needed and suggest some directions that appear to be especially promising.

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This paper analyzes how multinational enterprises respond to a restriction on interest deductions incurred for internal borrowing. The emphasis of the study is on a firm’s response with respect to external borrowing. The empirical investigation applies propensity score matching techniques and exploits the 2001 reform of the German thin-capitalization rule to solve endogeneity problems. The results suggest that restrictions on internal debt are associated with expansions in external debt finance, indicating a substitutional relationship. Since multinational enterprises can use internal debt to shift profits from high- to low-tax countries, this finding implies that policies aimed at securing corporate tax revenue possibly fail and should be subject to careful scrutiny by policymakers. JEL Code: G32, H25.

This paper reviews recent advances in the foundations of causal inference and introduces a systematic methodology for defining, estimating and testing causal claims in experimental and observational studies. It is based on non-parametric structural equation models (SEM) – a natural generalization of those used by econometricians and social scientists in the 1950-60s, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring the effects of potential interventions (also called “causal effects” or “policy evaluation”), as well as direct and indirect effects (also known as “mediation”), in both linear and non-linear systems. Finally, the paper clarifies the role of propensity score matching in causal analysis, defines the relationships between the structural and

The authors propose a strategy for studying the effects of time-varying instructional treatments on repeatedly observed student achievement. This approach responds to three challenges: (a) The yearly reallocation of students to classrooms and teachers creates a complex structure of dependence among responses; (b) a child's learning outcome under a certain treatment may depend on the treatment assignment of other children, the skill of the teacher, and the classmates and teachers encountered in the past years; and (c) time-varying confounding poses special problems of endogeneity. The authors address these challenges by modifying the stable unit treatment value assumption to identify potential outcomes and causal effects and by integrating inverse probability of treatment weighting into a four-way value-added hierarchical model with pseudolikelihood estimation. Using data from the Longitudinal Analysis of School Change and Performance, the authors apply these methods to study the impact of ''intensive math instruction'' in Grades 4 and 5.