3J

Course Content:

Building on students’ knowledge in simple linear regression, this course introduces more advanced statistical methods. We will focus on the following topics: 1) Subclassification, matching, and propensity score weighting as fundamental strategies to reduce confounding; 2) Common interpretations of the OLS estimator; 3) Robust inference with cluster-robust standard errors as well as bootstrap estimators; 4) Classical exposition of omitted variable bias and introduction to causal graphs to select control variables; 5) Instrumental variable estimation with two-stage least-squares; 6) Two-way fixed effects and the difference-in-difference estimator with panel data; 7) Mediation and moderation analysis. The course combines a theoretical introduction to each topic with lab sessions in which students perform replications of published work in Economics and Political Science using STATA. Students are encouraged to bring their own data sets and present their research projects and empirical analyses.

Course Objectives:

Students will develop a deeper understanding of the statistical problems that arise in applied research. It will give participants the skills to i) Make sensible choices about which data to collect; ii) Select an appropriate estimator for their estimands and the data at hand; iii) Precisely state the assumptions on which estimates are based; and iv) Conduct sensible, robust inferences and interpret their estimates accurately. More generally, students will be able to decide which variables they have to control for (and which they do not) and develop an understanding of what it means when regression results are distorted by selection bias or omitted variable bias.

Course Prerequisites:

This course is targeted at social and political scientists with a strong interest in applied empirical research and data analysis. Participants must be familiar with STATA and its command structure and be able to write their own do-files. R users are also welcome. The course is designed for students with basic training in statistics including linear regression and hypothesis testing. It is also essential that students have basic knowledge of matrix algebra, calculus, and probability theory to follow the lectures.

Core Reading:

– Angrist, J. D. and J.-S. Pischke (2009). Mostly Harmless Econometrics. An Empiricist’s Companion. Princeton: Princeton University Press.

Representative Background Reading:

– Alan Agresti and Barbara Finlay. Statistical Methods for the Social Sciences. Pearson, Upper Saddle River, 4th edition, 2009, Chapter 1-9.

Background knowledge required
Statistics
OLS = S

Maximum Likelihood Estimation: M

Computer Background
Stata = M

e = elementary, m = moderate, s = strong

Course Structure:

• Cause and Effect
• Subclassification, Weighting and Matching
• Perspectives on OLS
• Robust Inference with OLS
• Controls and Causal Graphs
• Instrumental Variables
• DID and Panel Data
• Moderation and Mediation
• Empirical Research: What matters?
• Student presentation

Essential Course Readings:

Day 1

– Angrist and Pischke (2009), Chapter 1-2.

– Holland (1986).

– Agresti and Finlay (2009), Chapter 5-6.

Day 2

– Cochran (1968).

– Rosenbaum (2009), Chapter 7, 8.1-8-3, 9.

Day 3

– Angrist and Pischke (2009), Chapter 3.

– Wooldridge (2010), Chapter 2.

Day 4

– Wooldridge (2009), Chapter 5, 8.

– Angrist and Pischke (2009), Chapter 8.

Day 5

– Morgan and Winship (2007), Chapter 3.

– Elwert and Winship (2014)

Day 6

– Angrist and Pischke (2009), Chapter 4.

– Wooldridge (2010), Chapter 5.

Day 7

– Angrist and Pischke (2009), Chapter 5.

– Wooldridge (2010), Chapter 10.

Day 8

– Baron and Kenny (1986)

– Imai et al. (2010)

Day 9

– Freedman (1991)

References:

Agresti, A., and B. Finlay. 2009. Statistical Methods for the Social Sciences. 4th ed. Upper Saddle River: Pearson.

Angrist, J. D., and J.-S. Pischke. 2009. Mostly Harmless Econometrics. an Empiricist’s Companion. Princeton: Princeton University Press.

Baron, R. M., and D. A. Kenny. 1986. “The Moderator–Mediator Variable Distinction in Social Psychological Research: Conceptual, Strategic, and Statistical Considerations.” Journal of Personality and Social Psychology 51(6), pp. 1173–1182.

Cochran, W. G. 1968. “The Effectiveness of Adjustment by Subclassification in Removing Bias in Observational Studies.” Biometrics 24(2), pp. 295–313.

Elwert, F. and C. Winship. 2014. Endogenous Selection Bias: The Problem of Conditioning on a Collider Variable. Annual Review of Sociology 40, pp. 31–53.

Freedman, D. A. 1991. “Statistical Models and Shoe Leather.” Sociological Methodology 21, pp. 291–313.

Holland, P. W. 1986. “Statistics and Causal Inference.” Journal of the American Statistical Association 81(396), pp. 945–60.

Imai, K., L. Keele, and D. Tingley. 2010. “A General Approach to Causal Mediation Analysis.” Psychological Methods 15(4), pp. 309–334.

Morgan, S. L., and C. Winship. 2007. Counterfactual and Causal Inference. Methods and Principles for Social Research. Cambridge: Cambridge University Press.

Rosenbaum, P. R. 2009. Design of Observational Studies. 2nd ed. New York: Springer.

Wooldridge, J. M. 2010. Econometric Analysis of Cross Section and Panel Data. 2nd ed. Cambridge: MIT Press.