Modelling and Analysis

This session reviews modelling and analysis and how it impacts the results of studies.

Objective

Underline the importance of modelling assumptions and of computing and reporting credible standard errors

Summary

Regression models and OLS estimation rest on a set of assumptions that ensure estimates are unbiased, efficient, and statistically valid. When these assumptions are not met, our estimates can become biased and our standard errors misleading, making inference unreliable. In this session, we review these modelling assumptions and discuss what happens when they fail. We then look at how different tools such as limited outcome models or clustering help us overcome implied issues and recover credible estimates.

Session Outline

• Introduction
  • Modelling assumptions and reliable SEs
• Modelling
  • Failures of Gauss-Markov conditions
  • Limited outcome models
  • Good/bad controls
• Analysis
  • The importance of SEs
  • Clustering
• Summaries
  • Of the session
  • Of the entire class

Materials

Open slides in html

Open slides in pdf

Specific resources for this lecture

Modelling

• A large share of the slides are derived from notes by Claire Palandri and related slides by Anna Papp
• Limited outcome models: Chapters 13 to 15 from Gelman, Hill, and Vehtari (2021)
• Bad controls: Chapter 3.2.3 of Angrist and Pischke (2009)

Clustering

• Articles:
  • MacKinnon, Nielsen, and Webb (2023)
  • Abadie et al. (2023) (and associated slides)
  • Bertrand, Duflo, and Mullainathan (2004)
• Courses:
  • Chapter 13 of Huntington-Klein (2022)
  • Chapter 2 of Cunningham (2021)

References

Abadie, Alberto, Susan Athey, Guido W Imbens, and Jeffrey M Wooldridge. 2023. “When Should You Adjust Standard Errors for Clustering?” The Quarterly Journal of Economics 138 (1): 1–35. https://doi.org/10.1093/qje/qjac038.

Angrist, Joshua D., and Jörn-Steffen Pischke. 2009. Mostly Harmless Econometrics: An Empiricist’s Companion. 1 edition. Princeton: Princeton University Press.

Bertrand, Marianne, Esther Duflo, and Sendhil Mullainathan. 2004. “How Much Should We Trust Differences-In-Differences Estimates?” The Quarterly Journal of Economics 119 (1): 249–75. https://doi.org/10.1162/003355304772839588.

Cunningham, Scott. 2021. Causal Inference: The Mixtape. Yale University Press. https://doi.org/10.2307/j.ctv1c29t27.

Gelman, Andrew, Jennifer Hill, and Aki Vehtari. 2021. Regression and Other Stories.

Huntington-Klein, Nick. 2022. The Effect: An Introduction to Research Design and Causality. 1st edition. Chapman and Hall/CRC.

MacKinnon, James G., Morten Ørregaard Nielsen, and Matthew D. Webb. 2023. “Cluster-Robust Inference: A Guide to Empirical Practice.” Journal of Econometrics 232 (2): 272–99. https://doi.org/10.1016/j.jeconom.2022.04.001.