Identification Strategies
Routing Summary
This folder covers quasi-experimental methods from MHE Chapters 4-6, plus Bayesian and advanced synthetic control methods, DAG-based causal identification, and Bayesian propensity score weighting. Contains 16 notes plus the Propensity Score Matching sub-topic.
- Need the classical Rosenbaum-Rubin propensity-score matching framework, caliper matching, covariate-balance and overlap diagnostics? → Propensity Score Matching
- Need instrumental variables or 2SLS? → Instrumental Variables
- Need LATE theorem or complier characterization? → Local Average Treatment Effects
- Need difference-in-differences or fixed effects? → Differences-in-Differences
- Need sharp/fuzzy RD designs? → Regression Discontinuity Designs
- Need Bayesian DiD with posterior over treatment effect? → Bayesian Difference in Differences
- Need synthetic control estimator with Python code? → Synthetic Control
- Need the linear factor model and bias bound theory? → Synthetic Control Bias Theory
- Need RMSPE inference, backdating, or leave-one-out checks? → Synthetic Control Inference and Diagnostics
- Need to assess if SC is appropriate for your setting? → Synthetic Control Requirements
- Need multiple treated units, bias correction, or matrix completion? → Synthetic Control Extensions
- Need GSC for multiple treated units with IFE model and bootstrap inference? → Generalized Synthetic Control Method
- Need DAG concepts, forks/chains/colliders, backdoor adjustment, d-separation? → DAGs and Causal Identification
- Need Bayesian inverse probability weighting / Liao-Zigler marginalization method? → Bayesian Propensity Score Weighting
Sub-topics
| Sub-topic | Notes | Covers |
|---|---|---|
| Propensity Score Matching | 5 | Propensity score & the balancing property (Rosenbaum-Rubin), matching methods & distance measures (nearest-neighbor, caliper, Mahalanobis, full/optimal), covariate balance diagnostics, common support / overlap — Stuart (2010) |
Concept Map
| Concept | Note | Type | Depends On | Key Result |
|---|---|---|---|---|
| 2SLS, Wald estimator, exclusion restriction | Instrumental Variables | concept | Omitted Variables Bias, Regression and the CEF, The Selection Problem, Conditional Independence Assumption | IV estimates causal effect for compliers when CIA fails |
| LATE theorem, compliers/always-takers/never-takers | Local Average Treatment Effects | concept | Instrumental Variables, The Selection Problem, The Experimental Ideal | IV estimates LATE, not ATE — only for compliers |
| Fixed effects, common trends, Card & Krueger | Differences-in-Differences | concept | The Selection Problem, Regression and the CEF, Conditional Independence Assumption, Omitted Variables Bias | DiD removes time-invariant unobserved confounders |
| Sharp and fuzzy RD, bandwidth choice | Regression Discontinuity Designs | concept | Instrumental Variables, Local Average Treatment Effects, Regression and the CEF, The Selection Problem | RD exploits threshold discontinuities for local causal effects |
| Bayesian DiD, posterior over treatment effect | Bayesian Difference in Differences | concept | Differences-in-Differences, The Selection Problem, The Experimental Ideal, Regression and the CEF | Full posterior over counterfactual and treatment effect |
| Synthetic control, donor pool, convex weights, placebo inference | Synthetic Control | concept | Differences-in-Differences, The Selection Problem, The Experimental Ideal | Weighted combination of untreated units estimates counterfactual for single treated aggregate |
| Linear factor model, bias bound, sparsity theorem, V-matrix | Synthetic Control Bias Theory | concept | Synthetic Control, The Selection Problem | Bias bounded by pre-treatment fit; convex hull projection guarantees sparsity |
| RMSPE ratio, permutation p-value, backdating, leave-one-out | Synthetic Control Inference and Diagnostics | concept | Synthetic Control, Synthetic Control Bias Theory | Permutation inference valid without asymptotic theory; RMSPE ratio detects poor donors |
| 5 contextual + 3 data requirements, when not to use SC | Synthetic Control Requirements | concept | Synthetic Control, Synthetic Control Bias Theory | SC needs large effect, clean comparison group, and pre-treatment fit within convex hull |
| Penalized SC, bias-corrected SC, elastic net, matrix completion | Synthetic Control Extensions | concept | Synthetic Control, Synthetic Control Bias Theory, Synthetic Control Inference and Diagnostics | Multiple extensions handle multiple treated units, sparse donors, and matrix completion |
| IFE model, ATT estimand, 3-step GSC, bootstrap inference | Generalized Synthetic Control Method | concept | Synthetic Control, Differences-in-Differences, The Selection Problem | GSC unifies DiD and SC via interactive fixed effects; valid for multiple treated units |
| DAGs, forks/chains/colliders, backdoor criterion, d-separation | DAGs and Causal Identification | concept | The Selection Problem, The Experimental Ideal | Valid adjustment set blocks all backdoor paths; do-calculus enables causal inference from observational data |
| Bayesian IPTW, Liao-Zigler marginalization, Rubin’s rules SE | Bayesian Propensity Score Weighting | concept | DAGs and Causal Identification, The Selection Problem, Bayesian Linear Regression | Marginalize over posterior propensity scores to incorporate treatment-model uncertainty |
Notes
- Mostly Harmless Econometrics - Overview — CONTAINS: Full book structure map, key concepts by chapter, cross-links to all identification strategy notes
- Instrumental Variables — CONTAINS: 2SLS estimation, Wald estimator, exclusion restriction, quarter-of-birth and draft lottery examples, first-stage F-test
- Local Average Treatment Effects — CONTAINS: LATE theorem, complier/always-taker/never-taker/defier taxonomy, characterizing compliers, external validity
- Differences-in-Differences — CONTAINS: Fixed effects regression, common trends assumption, Card & Krueger minimum wage, event studies
- Regression Discontinuity Designs — CONTAINS: Sharp and fuzzy RD, Lee incumbency example, Maimonides’ Rule, bandwidth selection, McCrary test
- Bayesian Difference in Differences — CONTAINS: PyMC implementation, posterior over treatment effect delta, explicit counterfactual prediction, parallel trends as model constraint
- Synthetic Control — CONTAINS: Formal potential outcomes setup, OLS weights (overfitting), constrained convex weights, scipy optimisation, California Proposition 99 cigarette tax example, placebo/permutation inference, Fisher’s exact test p-value
- Abadie 2021 - Overview — CONTAINS: Full paper structure map, German reunification running example, 5 key takeaways, links to all derived notes
- Synthetic Control Bias Theory — CONTAINS: Linear factor model (Eq. 10), bias bound theorem, sparsity theorem (convex hull projection), V matrix cross-validation, comparison with regression weights
- Synthetic Control Inference and Diagnostics — CONTAINS: RMSPE definition, RMSPE ratio (Eq. 12), permutation p-value, backdating definition, leave-one-out robustness
- Synthetic Control Requirements — CONTAINS: 5 contextual requirements (effect size, comparison group, no anticipation, no interference, convex hull), 3 data requirements, when not to use
- Synthetic Control Extensions — CONTAINS: Penalized SC for multiple treated units (Eq. 13), uniqueness/sparsity theorem, bias-corrected SC (Eq. 15–16), elastic net SC (Eq. 17–18), matrix completion methods
- Xu 2016 - Overview — CONTAINS: Paper overview, contribution summary, GSC vs DID/IFE/SC comparison table, caveats
- Generalized Synthetic Control Method — CONTAINS: IFE model Assumption 1, strict exogeneity Assumption 2, ATT estimand, 3-step GSC estimator, LOO cross-validation Algorithm 1, parametric bootstrap Algorithm 2, Monte Carlo performance (Table 1), EDR voter turnout example
- DAGs and Causal Identification — CONTAINS: Forks, chains, colliders, conditioning rules, d-separation formal definition, backdoor path definition, backdoor adjustment formula, valid adjustment sets, Simpson’s paradox
- Bayesian Propensity Score Weighting — CONTAINS: IPTW formula, pseudo-population interpretation, why Bayesian propensity scores are problematic (likelihood incompatibility), Liao-Zigler marginalization integral, brms R implementation, Rubin’s rules SE combination
Sources
- Mostly Harmless Econometrics.pdf — Mostly Harmless Econometrics (Angrist & Pischke, 2008), Chapters 4-6
- Difference in differences — PyMC example: Bayesian DiD with counterfactual inference
- 15 - Synthetic Control — Causal Inference for the Brave and True — Causal Inference for the Brave and True, Ch. 15: Synthetic control with Python (scipy, sklearn)
- Abadie 2021 - Using Synthetic Controls.pdf — Abadie (2021), JEL 59(2): 391–425. Authoritative methodological guide: feasibility, bias theory, inference, requirements, extensions
- Xu 2016 - Generalized Synthetic Control Method.pdf — Xu (2017), Political Analysis 25(1): 57–76. GSC method: IFE model, 3-step estimator, cross-validation, bootstrap inference, gsynth R package
- Unlock the Secrets of Causal Inference with a Master Class in Directed Acyclic Graphs — Graham Harrison, Towards Data Science (2023-04-06): DAGs, confounders, backdoor adjustment, d-separation
- How to use Bayesian propensity scores and inverse probability weights — Andrew Heiss (2021-12-18): Liao-Zigler Bayesian IPW in R/brms
See Also
- Data Collection Models — Bayesian perspective on experimental design
- Counterfactual Inference — Bayesian counterfactual prediction methods
- Nonparametric Causal Inference — BART + propensity scores for ATE/ATT estimation