This course covers the modern theory of causal inference from a social science perspective. We approach this topic by using causal graphs, which are extremely general and powerful theoretical devices to solve causal problems; at the same time, they are easy to understand. After the course, participants should better understand cutting-edge research, methodological discussions, and be able to improve the quality of their own research. Apart from that, the tools discussed in this course are also increasingly used by private companies. We start with a refresher of some basic probability theory. We then use causal graphs to understand problems like estimating causal effects, choice of control variables, selection bias, and testing causal assumptions, in nonparametric and in linear graphs. We then deal with effect heterogeneity and causal interactions. We conclude the first part by introducing counterfactuals, their connection to graphs and structural equations, and their application to decision-making problems. Throughout, we will discuss examples from research, business, and daily life. After this foundational part, we will find it easy to delve into two more advanced topics, instrumental variables and the analysis of causal mechanisms. Here, we focus more on discussing research applications. Towards the end of the course, participants have time to discuss how to use the tools covered in this course for their own research. Link to ZEUS.

Literature: Pearl, Judea, Madelyn Glymour, and Nicholas P. Jewell. Causal Inference in Statistics: A Primer. John Wiley & Sons, 2016.

#### 17.04. Why care? Plus probability refresher

#### 24.04. Graph Basics

#### 01.05. Labour Day (no class)

#### 08.05. Back-Door Criterion

#### 15.05. Multiple Interventions and the do-calculus

#### 22.05. Counterfactuals

#### 29.05. Mediation: Theory

#### 05.06. Mediation: Application

#### 12.06. Instrumental Variables: Theory

#### 19.06. Instrumental Variables: Application

#### 26.06. TBA

#### 03.07. TBA

#### 10.07. TBA

#### 17.07. TBA

Why causal inference is exciting and useful.

Necessary concepts from probability theory: Population, units, variables. Marginal PMF. Conditional probability. Independence. Law of total probability. Bayes' law. Expectations. Conditional expectations. Law of iterated expectations. Regression as a model for conditional expectations. Analgoue estimators.

Slides. Summary document of probability basics here. Problem Set.

We draw a lot and discuss what our drawings actually mean.

Topics: Graph terminology. d-separation. Structural Equations. Interventions and graph sugery.

We use graphs to understand whether and how we can learn about causal effects from data; and we illustrate some problems which have bothered many people for a long time, but are very easy to understand using graphs.

Topics: Linear graphs. Back-Door Criterion. Post-treatment and sample selection bias.

Slides. Problem Set for linear graphs. Problem Set for Back-Door Criterion.

We clarify even more things and suddenly we can also solve complicated problems very easily.

Topics: Covariate-specific effects. Multiple interventions/causal interactions. Back-door criterion for multiple interventions. Controlled direct effects including time-varying treatments and covariates. do-calculus.

Jay-Z leads us to counterfactuals AKA potential outcomes. As usual, everything is easy from a causal graph/structural causal model perspective.

Topics: Causal effects using counterfactuals. A new look at the identification problem with a simple economic model of whether you should attend university. Average treatment effect on the treated (ATT). Counterfactual interpretation of the back-door criterion. Graphical representation of counterfactuals..

What does it mean for something to have a "direct" or "indirect" effect?

Topics: Mediation in the linear case. Mediation in the nonparametric case. Policy relevance. Discrimination. Understanding identification assumptions using error terms, structural equations, potential outcomes. Sensitivity analysis under linearity. More general sensitivity analysis.

We discuss a few applications of mediation analysis in the social sciences.

The standard approach for when you have unobserved confounding.

Topics: Linear case. Nonparametric case. Manski and Balke/Pearl bounds. Identification assumptions using potential outcomes and graphs.

We discuss a few applications of instrumental variables in the social sciences.

This and following weeks: Backup. Participants have time to think about and discuss potential applications.

Further possible topics we may discuss, depending on interest: External validity; missing data; partial identification; discrimination and discriminatory algorithms; philosophical applications; networks and spillovers. Estimation (especially for mediation); sensitivity analysis; panel data