Design: Identification and Fixed Effects
Fixed effects are central to many econometric analyses. Here we discuss their nuts and bolts.
This session aims to provide a bird’s view of the conceptual framework used in causal inference analyses and to discuss how fixed effects work, under the hood.
Summary
Causal identification strategies are ways to form assumptions that may allow us to go from a quantity we can typically estimate in an applied economics study (the difference in average observed outcomes) to the quantity of interest, the Average Treatment effect on the Treated (ATT). Some of these strategies leverage repeated observations (DiD, event-study, etc) and make use of fixed effects. We discuss nuts and bolts of the use of fixed effects. In particular, they not only partial out variation but also change the interpretation of the coefficients being estimated and affect the variation used identifying variation. Additional challenges arise when using TWFEs.
Session Outline
- Notes on the Potential Outcomes Framework
- Overview of identification strategies based on repeated observations
- Some nuts and bolts of fixed effects (interpretation, projections and identifying variation)
- TWFE
Materials
Specific resources for this lecture
- A large share of the slides are derived from notes by Claire Palandri and related slides by Anna Papp.
- Chapter 16 to 19 of The Effect of Huntington-Klein (2022)
- Chapter 8 to 10 of Cunningham (2021)
- Aronow and Samii (2016) and Angrist and Pischke (2009) (section 3.3.1) interpret OLS regression as a weighted average of observations, depending on how well the endogenous variable of interest is correlated with other covariates.