Instructors
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.
Readings and textbooks
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:
- MHE: Angrist and Pischke, Mostly Harmless Econometrics: An Empiricist’s Companion, 2009, Princeton University Press.
- CIS: Imbens and Rubin, Causal Inference for Statistics, Social, and Biomedical Sciences, 2015, Cambridge University Press.
- TE Huntington-Klein, The Effect: An Introduction to Research Design and Causality, 2022, CRC Press.
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is the classic graduate-level text for causal inference, and is challenging but very accessible, though now a little out of date as it was published in 2009.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):
- CMRI: Pearl, Causality: Models Reasoning and Inference (2nd Ed), 2009, Cambridge University Press.
- CISAP: Pearl, Glymour, and Jewell, Causal Inference in Statistics: A Primer, 2016, Wiley.
- CIWI: Hernan and Robins, Causal Inference: What If, 2020, Routledge.
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 five problem sets, released at 5pm on Mondays using GitHub Classrooms. You must submit one week later at 11am, by pushing your repo, including your completed work as a rendered .pdf, to GitHub.
Summative assessment
The course will be assessed through two summative exercises:
- Quiz (40%, MY457/557): Monday, February 23rd, 13:15 - 14:15. Please consult timetables for venue.
This one-hour pen-and-paper quiz will cover all content from weeks 1 through 5. Further details will be provided in class.
AND
- Replication (60%, MY457): Due Friday, May 22nd 2026, 16:00. Please submit using GitHub Classroom. You will be provided 1 of 5 applied causal inference papers to critique, reappraise, and replicate.
OR
- Final Paper (60%, MY557): Due Friday, May 22nd 2026, 16:00. Please submit through Moodle. You will be expected to produce an original research paper, pre-analysis-plan, or independent replication and reappraisal, focused on causal inference.
Quick links to lectures
Quick links to seminars
Detailed course schedule
Note: Links to slides and code will be updated/added in advance of each week’s teaching.
1. Causal Frameworks
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.
Lecture
Readings
- MHE: Chapter 1
- CIS: Chapters 1, 2, and 3.1
- TE: Chapter 6
Additional readings
2. Randomization
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.
Lecture
Seminar: Causality and Randomization
Readings
- MHE: Chapter 2
- CIS: Chapters 3 & 4
- TE: Chapters 7 & 8
Additional readings
- CISAP: Chapter 3 OR CMRI: Chapters 3 & 4
3. Selection on Observables 1
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.
Lecture
Readings
- MHE: Chapter 3
- CIS: Chapters 12, 13, 18
- TE: Chapter 14
Additional readings
4. Selection on Observables 2
We consider the three most frequently seen estimation strategies for selection-on-observables designs: matching (including propensity scores), weighting, and regression.
Lecture
Seminar: Selection on Observables
Readings
- MHE: Sections 3.2 and 3.3
- CIS: Chapter 13
- TE: Chapter 14
Additional readings
5. Selection on Observables 3
We consider what happens if we are willing to weaken the assumptions underpinning our research designs, exploring partial identification and sensitivity analysis.
Lecture
Readings
- Manski, C.F., 1990. Nonparametric bounds on treatment effects. The American Economic Review, 80(2), pp.319-323. (very technical but worth reading, even if only for the intuition.)
- Imbens, G. W. (2003). Sensitivity to exogeneity assumptions in program evaluation. American Economic Review, 93(2), 126-132.
- Cinelli, C., & Hazlett, C. (2020). Making sense of sensitivity: Extending omitted variable bias. Journal of the Royal Statistical Society Series B: Statistical Methodology, 82(1), 39-67.
Additional readings
- Rosenbaum, P. R., & Rubin, D. B. (1983). Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome. Journal of the Royal Statistical Society: Series B (Methodological), 45(2), 212-218. (technical but foundational)
- Duarte, G., Finkelstein, N., Knox, D., Mummolo, J., & Shpitser, I. (2023). An automated approach to causal inference in discrete settings. Journal of the American Statistical Association, (just-accepted), 1-25. (very technical but very interesting)
6. Reading Week
7. Instrumental Variables 1
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.
Lecture
Readings
- TE: Chapter 19
- MHE: Chapter 4 OR CIS: Chapters 23 and 24
Additional readings
- Deaton, A. (2010). Instruments, randomization, and learning about development. Journal of economic literature, 48(2), 424-455.
- Imbens, G. W. (2010). Better LATE than nothing: Some comments on Deaton (2009) and Heckman and Urzua (2009). Journal of Economic literature, 48(2), 399-423.
- Angrist, J. D., Imbens, G. W., & Rubin, D. B. (1996). Identification of causal effects using instrumental variables. Journal of the American statistical Association, 91(434), 444-455.
- Andrews, I., Stock, J. H., & Sun, L. (2019). Weak instruments in instrumental variables regression: Theory and practice. Annual Review of Economics, 11, 727-753.
Seminar: Instrumental Variables
8. Instrumental Variables 2
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.
Lecture
Readings
Additional readings
- Goldsmith-Pinkham, P., Sorkin, I., & Swift, H. (2020). Bartik instruments: What, when, why, and how. American Economic Review, 110(8), 2586-2624.
- Borusyak, K., Hull, P., & Jaravel, X. (2022). Quasi-experimental shift-share research designs. The Review of Economic Studies, 89(1), 181-213.
- Frandsen, B., Lefgren, L., & Leslie, E. (2023). Judging judge fixed effects. American Economic Review, 113(1), 253-277.
9. Regression Discontinuity
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.
Lecture
Readings
Additional readings
- Lee, D. S., & Lemieux, T. (2010). Regression discontinuity designs in economics. Journal of economic literature, 48(2), 281-355. (strongly recommended)
- Keele, L. J., & Titiunik, R. (2015). Geographic boundaries as regression discontinuities. Political Analysis, 23(1), 127-155.
- If very interested, see:
- Cattaneo, M. D., Idrobo, N., & Titiunik, R. (2020). A practical introduction to regression discontinuity designs: Foundations. Cambridge University Press.
- Cattaneo, M. D., Idrobo, N., & Titiunik, R. (2024). A Practical Introduction to Regression Discontinuity Designs: Extensions. Cambridge: Cambridge University Press.
Seminar: Regression Discontinuity
10. Difference-in-Differences 1
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.
Lecture
Readings
- MHE: Section 5.2
- TE: Chapter 18
Additional readings
- Card, D., & Krueger, A. B. (1993). (1994). Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania. The American Economic Review, 84(4), 772-793. (foundational example)
- Bertrand, M., Duflo, E., & Mullainathan, S. (2004). How much should we trust differences-in-differences estimates?. The Quarterly journal of economics, 119(1), 249-275. (classic focused on inference)
- Roth, J. (2022). Pretest with caution: Event-study estimates after testing for parallel trends. American Economic Review: Insights, 4(3), 305-322. (technical, focused on issues with pre-trend tests)
11. Difference-in-Differences 2
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.
Lecture
Readings
- Baker, A. C., Larcker, D. F., & Wang, C. C. (2022). How much should we trust staggered difference-in-differences estimates?. Journal of Financial Economics, 144(2), 370-395. (has some quite accessible discussions)
- Roth, J., Sant’Anna, P. H., Bilinski, A., & Poe, J. (2023). What’s trending in difference-in-differences? A synthesis of the recent econometrics literature. Journal of Econometrics. (technical but a good overview)
- TE: Chapter 18, especially 18.3
Additional readings
- Goodman-Bacon, A. (2021). Difference-in-differences with variation in treatment timing. Journal of Econometrics, 225(2), 254-277. (very technical but parts can be read quite easily)
- Callaway, B., & Sant’Anna, P. H. (2021). Difference-in-differences with multiple time periods. Journal of econometrics, 225(2), 200-230.
- Liu, L., Wang, Y., & Xu, Y. (2024). A practical guide to counterfactual estimators for causal inference with time‐series cross‐sectional data. American Journal of Political Science, 68(1), 160-176.
- Dube, A., Girardi, D., Jorda, O., & Taylor, A. M. (2023). A local projections approach to difference-in-differences event studies (No. w31184). National Bureau of Economic Research.
- Abadie, A., (2021). Using synthetic controls: Feasibility, data requirements, and methodological aspects. Journal of economic literature, 59(2), pp.391-425.
Seminar: Difference-in-Differences
[COURSE ENDS]