Methods of Modern Causal Analysis Based on Observational Data

The central aim of this course is to empower you to think about causality and to apply new tools of modern causal analysis in your own research.

Experiments tend to be 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 they have several potential pitfalls that pose threats to the internal and external validity.

For ethical and practical reasons, experiments are often not feasible in social sciences. This course will therefore focus on modern methods of causal inference based on non-experimental data.

The course is structured around four key topics:

1. I present the general idea of causality based on the potential outcome framework and directed acyclic graphs (DAGs).
2. I introduce linear regression and propensity score matching (PSM) as methods of modern causal analysis for cross-sectional data that rely on the crucial assumption of selection on observed variables.
3. I present instrumental variables (IV) estimators that can deal with the problem of selection on unobserved variables.
4. We discuss basic and advanced topics of the fixed-effect logic and difference-in-differences (DID) approaches that use the benefits of longitudinal data.

Rather than get lost in the details of mathematical proofs and philosophical debates, the course offers an applied introduction and hands-on experience in lab sessions.

We will discuss the strengths and limitations of each approach, and I will illustrate them using examples from the social science literature.

 I Causality, Counterfactuals and Causal Graphs

How can we define causality in social science research? This course starts with one of the most important, basic questions of the philosophy of science.

You will learn to distinguish different kinds of causal hypotheses and reflect on the basic conditions considered important for making causal claims.

Researchers often try to avoid making causal inferences, but based on practical examples from applied research, I will show 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 you will also learn how to pose properly formulated questions about causal effects. But you will also critically discuss the basic assumptions of counterfactuals, manipulability and the stable unit treatment value assumption (SUTVA).

Directed acyclic graphs (DAGs) offer an illustrative graphical approach to the problem of causal inference. We will use them to clarify the crucial difference between (self-)selection processes into the X-variable of interest based on observed variables versus unobserved variables.

We will discuss advanced topics of endogenous selection bias, common-cause confounding and overcontrol bias in the framework of DAGs.

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

The most common non-experimental method 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.

You will apply your new knowledge about counterfactuals to understand linear regression in the notation of potential outcomes.

Applying the principles of DAGs, you 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 over MLR.

Applying your knowledge on the counterfactual model and DAGs, you will learn how to implement the different steps of PSM.

I will explain 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. We will apply the different steps based on real-world data in a computer lab session. We will then briefly discuss differences between the PSM approach and other matching approaches.

We conclude with 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. You will critically discuss examples of instrumental variables from the applied research 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.

In a lab session you will learn how to implement IV estimators in Stata based on real-world data, and how to interpret the results.

We will place special emphasis on critical discussion of the validity of IV approach assumptions in the context of practical research examples.

IV Using Longitudinal Data: The Fixed-Effect Logic and the Difference-in-Differences (DID) Approach

When prospective or retrospective longitudinal data, i.e. repeated measurements of the outcome Y-variable, are available, we can use other approaches to deal with the problem of selection on observable and unobservable variables.

The true strength of longitudinal data is that it allows us to observe the outcomes of the same observational unit over time.

In contrast to the random effect approach, we can easily remove time-constant observed and unobserved characteristics of the observational unit when applying the logic of before-after or fixed-effect panel estimators, and we can model anticipation effects and the impact function of the treatment.

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.

You will learn how to apply the DID estimator in a linear regression design, and how to combine the DID estimator with PSM to construct the control group in an innovative way.

You will apply your knowledge of causal graph analysis in the longitudinal context to discuss advanced topics such as the potential biases induced by introducing a lagged dependent variable.

In a lab session you will learn how to implement DID-regression and DID-PSM estimators in Stata based on real-world data, and how to interpret the results.

I expect you to be familiar with the basics of statistics and multiple linear regression analysis.

Empirical applications will be implemented in Stata, so knowledge of Stata is helpful but not a prerequisite because pre-programmed data sets and full syntax codes will be provided.