Course Website for Winter Term 2025
Office hour may be booked via LSE’s StudentHub. If you have questions or concerns about class material, problem sets, or the exam, please use the class forum on Moodle. We will generally not reply to emails about the course material, but we will reply promptly to questions posted on the forum. Of course, if you questions or concerns are of a private or personal nature, please email or attend office hours.
There is a reasonable amount of reading for this class, especially in the early weeks. You are strongly encouraged to do the reading before class, paying close attention to details (i.e., do not skim over equations). In addition to some key articles, throughout the term we will dip into three main textbooks, which we will refer to by their acronyms:
Note: The three textbooks have very different flavours, and are pitched at different technical levels. MHE is the classic graduate-level text for causal inference, and is challenging but very accessible, though now a little out of date as it was published in 2009. CIS is very dense and very technical, and serves as a reference text for much of the foundational material in the class (weeks 1-5). TE is the most accessible textbook and is very applied, while being lighter on details and generally less technically focused. The reading list is designed to allow you pick your own adventure, to a degree.
If you are particularly interested in the course material, there will be additional readings set from the following textbooks (as well as a few articles):
Note: if you are particularly interested in graphical models and their application to causal inference, it is strongly recommended that you do all the readings from either CMRI or CISAP. CMRI is extremely technical and dense, while CISAP is a gentler (though not that gentle) introduction to some of the basics introduced in CMRI. If there are suggested readings from both books, you should choose either, not both.
Statistics is best learned by doing. There will be six problem sets, released at 5pm on Wednesdays. You must submit one weeks later at 11am, on Moodle. Your submission should be written in RMarkdown, and must be a knitted .pdf, formatted as shown in this problem set template, which produces a pdf that looks like this. If you do not follow the formatting requirements your problem set will not be marked. Comments will be returned via Moodle within two weeks of submission.
| Type | Release date | Due date | |
|---|---|---|---|
| 1 | Formative problem set 1 | 29 January 2025 - 5pm | 5 February 2025 - 11am |
| 2 | Formative problem set 2 | 12 February 2025 - 5pm | 19 February 2025 - 11am |
| 3 | Formative problem set 3 | 5 March 2025 - 5pm | 12 March 2025 - 11am |
| 4 | Formative problem set 4 | 19 March 2025 - 5pm | 26 March 2025 - 11am |
| 5 | Formative problem set 5 | 2 April 2025 - 5pm | 9 April 2025 - 11am |
| Week | Topic |
|---|---|
| 2 | Causality and Randomization |
| 4 | Selection on Observables |
| 7 | Instrumental Variables |
| 9 | Regression Discontinuity |
| 11 | Difference-in-Differences |
Note: Links to slides and code will be updated/added in advance of each week’s teaching.
We begin with an introduction to the class, both substantively and administratively.
We then introduce the potential outcomes framework, which will provide the technical foundations that are used throughout the rest of the class. We will also briefly introduce the graphical model for causal inference.
We introduce the concept of randomization and its value for causal inference. We discuss, at a high level, design, analysis, and inference for randomized experiments.
We depart from the safe shores of controlled randomization, into the treacherous waters of observational research design. We will begin with a theoretical exploration of the selection on observables design (SOO) – its assumptions and identification results – using both potential outcomes and graphical theory.
We consider the three most frequently seen estimation strategies for selection-on-observables designs: matching (including propensity scores), weighting, and regression.
We consider what happens if we are willing to weaken the assumptions underpinning our research designs, exploring partial identification and sensitivity analysis.
We now move onto a new research design: instrumental variables (IV). We introduce the basic architecture of modern IV, learn about the various assumptions needed to admit a causal interpretation, and explore some of the weaknesses and fragilities of the approach.
Extending our investigation of IV designs, we focus on the interpertation and estimation of continuous IV settings, shift-share (Bartik) instruments, examiner designs, and recentered IV.
We move to the next core research design, regression discontinuity (RD), considering modern approaches to both sharp and fuzzy RD settings. We briefly consider the regression kink (RK) design.
We now introduce one of the most popular research designs for applied causal inference, difference-in-differences (DiD). We consider cases in which a treatment is rolled out such that we have variation over two dimensions: time and units. We focus almost exclusively on canonical cases in which we have only two time-periods and two treatment groups of units. We will close by briefly considering falsification tests in situations with two pre-treatment periods. Diverging from the previous approaches in which we rely on assumptions about the nature of treatment assignment, we introduce new assumptions about trends in potential outcomes over time.
We continue our exploration of DiD, broadening our focus to cases with more than 2 time periods. We discuss first the two-way fixed effects estimator that has been a dominant tool for estimating ‘generalised difference-in-differences’ and then explore the implied assumptions in this approach and its weaknesses, specifically for staggered and non-saturating treatments, and cases with heterogeneous treatment effects. We introduce alternative ‘modern’ estimators that are robust to these settings. We conclude with a very brief foray into the synthetic control method.
[COURSE ENDS]