The estimation of causal effects: an introduction to methods of causal inference based on peer effects in education

This article discusses the problem of causal inference based on contextual peer effects in education. For this purpose, I first introduce the counterfactual approach to causality and the fundamental problem of causal inference. Subsequently, experiments and a number of statistical methods are discussed as possible approaches to estimate causal effects. In particular, conditioning on observables using common linear regression models as well as matching procedures (such as propensity score matching), fixed-effects models, the difference-in-difference approach, instrumental variables, and the regression discontinuity design are discussed. The introduction of these methods is neither focused on the mathematical background nor on the estimation procedure but rather on the general logic and the assumptions connected with a causal interpretation of the estimated effects. The paper closes with an analysis of compositional peer effects in German elementary schools to illustrate the adequate treatment of selection processes.