Methods of Modern Causal Analysis Based on Observational Data

The central aim of this course is to empower participants to think about causality and to apply new tools of modern causal analysis in their own research. Experiments are seen as the gold standard for drawing causal inference because of the manipulation of the treatment and the random assignment to the treatment groups. But there are several potential pitfalls of experiments that pose threats to the internal and external validity. Moreover, since experiments are often not feasible in social sciences due to ethical and practical reasons, this course will focus on modern methods of causal inference based on non-experimental data. The course content is structured around four key topics: First, the general idea of causality is presented based on the potential outcome framework and directed acyclic graphs (DAGs). Second, linear regression and propensity score matching (PSM) are introduced as methods of modern causal analysis for cross-sectional data that rely on the crucial assumption of selection on observed variables. Third, instrumental variables (IV) estimators are presented that can deal with the problem of selection on unobserved variables. Fourth, difference-in-difference (DID) approaches are discussed that use the benefits of longitudinal data. Instead of getting lost in the details of mathematical proofs and philosophical debates, the course offers an applied introduction and hands-on experience in lab sessions. Strengths and limitations of each approach will be discussed and illustrated with examples from the social science literature.

In the following, a detailed course outline is provided:

(I) Causality, Counterfactuals and Causal Graphs

How can we define causality in social science research? Starting with this basic question this course starts with one of the most important questions of the philosophy of science. Participants will learn to distinguish different kinds of causal hypotheses and they will reflect on the basic conditions that are seen as important for making causal claims. Although researchers often try to avoid making causal inferences, based on practical examples from applied research it will be shown that any serious research hypothesis postulates explicitly or, at least, implicitly a causal relationship between two or more variables.

The first class will introduce Rubin’s notation of potential outcomes, which has become the backbone of modern causal analysis in social sciences because it clearly defines different types of causal effects (the ATT, ATNT and ATE) and allows for causal effect heterogeneity. Based on this model participants will also learn how to pose properly formulated questions about causal effects. But participants will also critically discuss the basic assumptions of counterfactuals, manipulability and the stable unit treatment value assumption (SUTVA). Moreover, directed acyclic graphs (DAGs) will be introduced because they offer an illustrative graphical approach to the problem of causal inference. They will be used to clarify the crucial difference between (self-)selection processes into the X-variable of interest based on observed variables versus unobserved variables. Advanced topics of endogenous selection bias, common-cause confounding and overcontrol bias will be discussed in the framework of DAGs.

(II) Selection on Observables: Multiple Linear Regression (MLR) and Propensity Score Matching (PSM)

Regarding non-experimental methods, the most prominent approach is multiple linear regression (MLR) analysis. Its strategy is to condition on observable confounding variables in order to disentangle the causal effect of X on Y. However, in practice, researchers often control for the wrong variables and neglect important control variables because they are not aware of modern causal analysis. Participants will apply their new knowledge about counterfactuals to understand linear regression in the notation of potential outcomes. Moreover, applying the principles of DAGs participants will learn how to select the right control variables in a linear regression based on examples of applied research.

Propensity Score Matching (PSM) is an alternative method to condition on selection on observables, which has several advantages compared to MLR. Applying their knowledge on the counterfactual model and DAGs, participants will learn how to implement the different steps of PSM. Specifically, it will be explained how to estimate propensity scores, how to implement and choose between different matching and estimation options and how to test whether PSM succeeded in balancing the observed control variables. The different steps will be applied based on real-world data in a computer lab session. Differences between the PSM approach and other matching approaches will be shortly discussed. This section will conclude by an outlook on model extensions such as multiple treatments or sensitivity analysis in terms of Rosenbaum bounds.

(III) Selection on Unobservables: The Instrumental Variable (IV) Approach

MLR and PSM will produce biased estimates of causal effects if there is selection into the X-variable of interest based on unobserved factors. Instrumental variables (IV) are seen as a solution to this problem. Its underlying identification strategy is to find an instrumental variable that is correlated with the X-variable of interest without having an independent effect on the outcome Y-variable. This course introduces IV estimators based on the counterfactual model and DAGs. Participants will critically discuss examples of instrumental variables from the applied research in order to understand the problems of IV estimators (weak instruments, violation of exclusion restrictions etc.).

This course will move beyond the classical textbooks on IV by introducing Angrist’s alternative interpretation of the IV estimator as identifying a Local Average Treatment Effect (LATE) in the context of heterogeneous effects, which is more reasonable for applications in social sciences. Moreover, model extensions in terms of the control function (CF) estimator can even identify the ATE by making distributional assumptions about the error terms. This approach explicitly models the selection processes into the X-variable of interest. As Winship and Morgan (1992) argue selectivity is not only a source of bias in research, but also a genuine theoretical idea in social science because selectivity results naturally from human behavior such as individuals’ decisions/choices. In a lab session participants will learn how to implement IV and CF estimators in Stata based on real-world data and how to interpret the results. A special emphasis will lay on the critical discussion of the validity of the assumptions of both the IV and CF approach in the context of practical research examples.

(IV) Using Longitudinal Data: The Difference-in-Differences (DID) Approach

When prospective or retrospective longitudinal data, i.e. repeated measurements of the outcome Y-variable, are available additional approaches can be employed to deal with the problem of selection on observable and unobservable variables. The true strength of longitudinal data lies in the possibility to observe the outcomes of the same observational unit over time. Thus, applying the logic of before-after or fixed-effect panel estimators, time-constant observed and unobserved characteristics of the observational unit can be easily removed. The difference-in-differences (DID) approach combines this fixed-effect logic with a control group comparison. Comparing time trends in the outcome Y-variable in the so called treatment and control group allows for eliminating not only time-constant individual effects but also common time trends. Participants will not only learn how to apply the DID estimator in a linear regression design but also how to combine the DID estimator with the method of propensity score matching (PSM) in an innovative way. Using the PSM logic is an innovative strategy to form an appropriate control group in the DID design. In a lab session participants will learn how to implement the DID-regression and the DID-PSM estimators in Stata based on real-world data and how to interpret the results.

Participants are expected to be familiar with the basics of statistics and they should be familiar with multiple linear regression analysis. Empirical applications will be implemented in Stata. Therefore, any knowledge of Stata is very helpful. However, it is not a prerequisite because pre-programmed data sets and full syntax codes will be provided.