Math 590S Causal Inference. Fall 2022.

• Instructor: Xingye Qiao

• Email: xqiao@binghamton.edu

• Office: WH-134

• Meeting time & location: TR 8:30 at WH 100E.

• Office hours: Fridady 10 to 11. I should usually be in my office but you are recommended to email me to confirm just in case.

Prerequisite

This course requires you to have a background in regression (e.g., linear and logistic models) at the level of Math 455 or Math 531. Additionally, some background in statistical theory at the level of Math 502 (or Math 488 as a minimum), and some background in machine learning at the level of Math 457 or Math 535 are helpful but not strictly required. Students should have some programming experience using a language such as R, Python, Julia, SAS, or MATLAB.

Description

Although most statistical inference practices focus on associational relationships among variables, in many contexts the goal is to establish the causal effect of an intervention or treatment. Almost every domain has significant causal research questions that can drive decision-making (e.g. labor economics, epidemiology, marketing, political science). What exactly is causation and how can it be determined whether an observed relationship is truly causal? How can we draw causal conclusions from data? In this course students will learn the fundamentals of how to reason about causality and make causal determinations using empirical data.

The course will begin by introducing the counterfactual framework (also known as the potential outcomes Neyman-Rubin Causal Model) of causal inference and then discuss a variety of approaches, starting with the most basic experimental designs to more complex observational methods, for making inferences about causal relationships from the data. For each approach, we will discuss the necessary assumptions that a researcher needs to make about the process that generated the data, how to assess whether these assumptions are reasonable, and finally how to interpret the quantity being estimated.

The methodologies and theory covered in this course possess a broad scope of applications, ranging from the physical, life, social, and management sciences, to engineering, among others. Conceptual understanding, not necessarily memorization or theoretical derivations of equations, is required and emphasized throughout the course. Applications are drawn from a variety of fields including political science, economics, sociology, public health, and medicine. This course is a mix of statistical theory and data analysis. Students will be exposed to statistical questions that are relevant to decision and policy making.

Topics include: the fundamental components of the potential outcomes Neyman-Rubin Causal Model, Fisherian randomization-based causal inference, Neymanian repeated sampling-based causal inference, drawing causal inferences from linear regression models, the design and analysis of observational studies, propensity score, subclassification, matching, weighting, doubly-robust estimation, non-binary treatment, design and analysis for Big Observational Data using machine learning, sensitivity analyses, instrumental variables, principal stratification, regression discontinuity designs, difference-in-differences, and the Bayesian paradigm for causal inference. Topics and the course outline are subject to change as the semester progresses.

Recommended Texts

Imbens G.W., Rubin D.B. (2015). Causal Inference for Statistics, Social, and Biomedical Sciences. Cambridge University Press.

Hernán M.A., Robins J.M. (2020). Causal Inference: What If. Boca Raton: Chapman & Hall/CRC. (online PDF available)

Angrist, J.D., & Pischke, J.S. (2009). Mostly Harmless Econometrics: An Empiricist's Companion. Princeton University Press.

Morgan, S.L., & Winship, C. (2015). Counterfactuals and Causal Inference. Cambridge University Press.

Piazza

Please use Piazza (www.piazza.com) for all electronic communications with me rather than email. Piazza is a question-and-answer platform. It supports LaTeX, code formatting, embedding of images, and attaching of files. You are encouraged to ask questions when you have difficulty understanding a concept or working around a piece of code – you can even ask questions anonymously. Moreover, you can also answer questions from your classmates. I constantly monitor the answers and endorse those which make more sense to me. Announcement will be sent to the class using Piazza. All enrolled students should create an account with Piazza (www.piazza.com) by visiting their website. Click “enroll now” and select “Binghamton University,” then search for “Math 590S.”

Brightspace

Brightspace will only be used for recording grades on assignments and exams and for distributing solutions. The code and lecture notes can also be found on the Brightspace.

Grading

• Homework (40%)

• Literature Project (25%)

• Final project (35%)

Literature Project

Each student will be assigned a paper from either the statistics literature or a domain-area journal to read and report on to the class. Students will give a short presentation, 15-20 minutes, and write a short paper summarizing the main points of the manuscript. Each of the assigned papers will be related to the content of this course; some manuscripts will be extensions of topics that are covered in the course while others go beyond the topics covered in class but should be easily understood by someone in this course. In both the paper and presentation, you are to summarize, in your own words, a high-level description of the main findings and results of the manuscript. The target audience for this assignment is someone with advanced training in causal inference (as in the students of this course) but that may not be familiar with this particular line of research. You should not attempt to reiterate all the mathematical development of the manuscript or show the derivations of proofs or theorems; there is simply not space or time to do that nor is that particularly helpful in capturing the main ideas of the manuscript. You should concentrate on giving the main results of the manuscript and discussing why these results are important. These presentations will be given throughout the semester so the due dates will vary by student.

Papers

Chapter 3.5: Doubly robust estimation

• Hirano, K., Imbens, G. W., & Ridder, G. (2003). Efficient estimation of average treatment effects using the estimated propensity score. Econometrica, 71(4), 1161–1189.

• Mercatanti, A., & Li, F. (2014). Do debit cards increase household spending? Evidence from a semiparametric causal analysis of a survey. The Annals of Applied Statistics, 8(4), 2485–2508.

• Mao, H., Li, L., & Greene, T. (2019). Propensity score weighting analysis and treatment effect discovery. Statistical Methods in Medical Research, 28(8), 2439–2454.

Chapter 3.6: Non-binary Treatment

• Meng, H., & Qiao, X. (2022). Augmented direct learning for conditional average treatment effect estimation with double robustness. Electronic Journal of Statistics, 16, 3523-3560.

• Flores, Flores-Lagunes, Gonzalez, Neumann (2012): Estimating the Effects of Length of Exposure to Instruction in a Training Program: The Case of Job Corps. Review of Economics and Statistics. 94(1): 153-171.

Chapter 4: Machine Learning

• Imai, K., & Ratkovic, M. (2013). Estimating treatment effect heterogeneity in randomized program evaluation. The Annals of Applied Statistics, 7(1), 443-470.

• Qian, M., & Murphy, S. A. (2011). Performance guarantees for individualized treatment rules. Annals of statistics, 39(2), 1180.

• Johansson, F., Shalit, U., & Sontag, D. (2016, June). Learning representations for counterfactual inference. In International conference on machine learning (pp. 3020-3029). PMLR.

• Farrell, M. H., Liang, T., & Misra, S. (2021). Deep neural networks for estimation and inference. Econometrica, 89(1), 181-213. (This is a theory paper.)

• Yao, L., Li, S., Li, Y., Huai, M., Gao, J., & Zhang, A. (2018). Representation learning for treatment effect estimation from observational data. Advances in Neural Information Processing Systems, 31.

• Shi, C., Blei, D., & Veitch, V. (2019). Adapting neural networks for the estimation of treatment effects. Advances in neural information processing systems, 32.

• Roberts, M. E., Stewart, B. M., & Nielsen, R. A. (2020). Adjusting for confounding with text matching. American Journal of Political Science, 64(4), 887-903.

• Alaa, A. M., Weisz, M., & Van Der Schaar, M. (2017). Deep counterfactual networks with propensity-dropout. arXiv preprint arXiv:1706.05966.

Final Project

As a final project, students will either analyze a data set using some of the methods for causal inference that we discuss or conduct a small numerical study (simulation or real data example) to verify the theoretical properties of a method or an extension of a method discussed in this course. The findings will be written-up in a short paper. More on this assignment will be given later. The project will be due at the time of the final exam for this course.