Regression Foundations
Routing Summary
This folder covers regression mechanics and interpretation from MHE Chapter 3. Contains 3 notes.
- Need the CEF and why regression approximates it? → Regression and the CEF
- Need when regression is causal (selection on observables)? → Conditional Independence Assumption
- Need the OVB formula and direction of bias? → Omitted Variables Bias
Concept Map
| Concept | Note | Type | Depends On | Key Result |
|---|---|---|---|---|
| Regression as best linear approximation to CEF, Frisch-Waugh, robust SEs | Regression and the CEF | concept | The Selection Problem, The Experimental Ideal, Research Questions in Econometrics | Regression is the minimum MSE linear approximation to the CEF |
| CIA / selection on observables: when regression is causal | Conditional Independence Assumption | concept | Regression and the CEF, The Selection Problem, The Experimental Ideal | CIA + overlap → regression estimates causal effects |
| OVB formula, direction of bias, schooling example | Omitted Variables Bias | concept | Regression and the CEF, Conditional Independence Assumption, The Selection Problem | OVB = (effect of omitted var) x (relationship to included var) |
Notes
- Regression and the CEF — CONTAINS: Conditional expectation function, regression as CEF approximation, Frisch-Waugh theorem, robust standard errors, saturated models
- Conditional Independence Assumption — CONTAINS: CIA / selection on observables, overlap condition, propensity score, matching, when regression is causal
- Omitted Variables Bias — CONTAINS: OVB formula, short vs long regression, direction of bias, schooling returns example, bad controls
Sources
- Mostly Harmless Econometrics.pdf — Mostly Harmless Econometrics (Angrist & Pischke, 2008), Chapter 3
See Also
- Bayesian Linear Regression — Bayesian perspective on the same regression concepts
- Spurious Association and Confounds — DAG-based approach to confounding (Statistical Rethinking)