|
63 | 63 | "cell_type": "markdown", |
64 | 64 | "id": "4d734cd9", |
65 | 65 | "metadata": {}, |
66 | | - "source": [ |
67 | | - "## What Makes EDiD Different?\n", |
68 | | - "\n", |
69 | | - "Consider a staggered adoption design with cohorts treated at periods 3, 5, and 7, plus a never-treated group. To estimate ATT(g=5, t=6), **Callaway-Sant'Anna** uses a single 2x2 comparison:\n", |
70 | | - "\n", |
71 | | - "> *Compare the outcome change from period 4 to 6 for cohort 5 versus the never-treated group.*\n", |
72 | | - "\n", |
73 | | - "But under **PT-All** (parallel trends across all pre-treatment periods), there are *additional* valid comparisons. Cohort 7 is also untreated at period 6, so it can serve as a comparison group too. And periods 1, 2, 3 can all serve as valid baselines, not just period 4.\n", |
74 | | - "\n", |
75 | | - "Each of these comparisons provides an unbiased estimate of ATT(g=5, t=6), but with different variances. **EDiD finds the optimal linear combination** --- the one that minimizes variance --- by computing the inverse covariance matrix of these \"generated outcomes\" (the paper calls this $\\Omega^*$).\n", |
76 | | - "\n", |
77 | | - "The result: **same point estimates as CS under PT-Post**, but **tighter standard errors under PT-All** because EDiD exploits the overidentification.\n", |
78 | | - "\n", |
79 | | - "> **Key equation (for the curious):** The efficient weight vector is $w^* = \\frac{\\mathbf{1}' \\Omega^{*-1}}{\\mathbf{1}' \\Omega^{*-1} \\mathbf{1}}$, where $\\Omega^*$ is the covariance matrix of the generated outcomes across all valid (comparison group, baseline) pairs. This is the classic GLS optimal weighting. See REGISTRY.md or the paper for full derivations." |
80 | | - ] |
| 66 | + "source": "## What Makes EDiD Different?\n\nConsider a staggered adoption design with cohorts treated at periods 3, 5, and 7, plus a never-treated group. To estimate ATT(g=5, t=6), **Callaway-Sant'Anna** uses a single 2x2 comparison:\n\n> *Compare the outcome change from period 4 to 6 for cohort 5 versus the never-treated group.*\n\nBut under **PT-All** (parallel trends across all pre-treatment periods), there are *additional* valid comparisons. Cohort 7 is also untreated at period 6, so it can serve as a comparison group too. And periods 1, 2, 3 can all serve as valid baselines, not just period 4.\n\nEach of these comparisons provides an unbiased estimate of ATT(g=5, t=6), but with different variances. **EDiD finds the optimal linear combination** --- the one that minimizes variance --- by computing the inverse covariance matrix of these \"generated outcomes\" (the paper calls this $\\Omega^*$).\n\nThe result: **matching post-treatment ATT(g,t) with CS under PT-Post**, but **tighter standard errors under PT-All** because EDiD exploits the overidentification.\n\n> **Key equation (for the curious):** The efficient weight vector is $w^* = \\frac{\\mathbf{1}' \\Omega^{*-1}}{\\mathbf{1}' \\Omega^{*-1} \\mathbf{1}}$, where $\\Omega^*$ is the covariance matrix of the generated outcomes across all valid (comparison group, baseline) pairs. This is the classic GLS optimal weighting. See REGISTRY.md or the paper for full derivations." |
81 | 67 | }, |
82 | 68 | { |
83 | 69 | "cell_type": "markdown", |
|
499 | 485 | "cell_type": "markdown", |
500 | 486 | "id": "ef99ee47", |
501 | 487 | "metadata": {}, |
502 | | - "source": "## Summary\n\n**Key takeaways:**\n\n1. EDiD achieves the **semiparametric efficiency bound** for ATT estimation in staggered designs\n2. Under **PT-All**, EDiD exploits overidentification for tighter SEs than CS\n3. Under **PT-Post**, EDiD matches CS for post-treatment ATT(g,t); pre-treatment diagnostics use a fixed baseline and may differ from CS's default varying baseline\n4. The efficiency gain comes from optimally weighting across all valid (comparison group, baseline) pairs\n5. **Event study** and **group** aggregations work just like CS\n6. **Multiplier bootstrap** provides robust inference with Rademacher, Mammen, or Webb weights\n7. **Condition numbers** flag potentially unstable weight matrices\n8. **Anticipation** shifts the effective treatment boundary for pre-treatment effects\n9. Phase 1 is **no-covariates only** --- Phase 2 will add covariate support\n10. When in doubt, run both EDiD and CS --- if ATTs agree, report EDiD for tighter CIs\n\n**Parameter reference:**\n\n| Parameter | Default | Description |\n|-----------|---------|-------------|\n| `pt_assumption` | `\"all\"` | `\"all\"` (overidentified) or `\"post\"` (just-identified, matches CS post-treatment ATT) |\n| `alpha` | `0.05` | Significance level |\n| `n_bootstrap` | `0` | Number of bootstrap iterations (0 = analytical only) |\n| `bootstrap_weights` | `\"rademacher\"` | Bootstrap weight distribution: `\"rademacher\"`, `\"mammen\"`, `\"webb\"` |\n| `seed` | `None` | Random seed for reproducibility |\n| `anticipation` | `0` | Anticipation periods |\n\n**Reference:** Chen, X., Sant'Anna, P. H. C., & Xie, H. (2025). Efficient Difference-in-Differences and Event Study Estimators. *Working Paper*.\n\n*See also: [Choosing an Estimator](../choosing_estimator.rst) for guidance on when to use EDiD vs other estimators.*" |
| 488 | + "source": "## Summary\n\n**Key takeaways:**\n\n1. EDiD achieves the **semiparametric efficiency bound** for ATT estimation in staggered designs\n2. Under **PT-All**, EDiD exploits overidentification for tighter SEs than CS\n3. Under **PT-Post**, EDiD matches CS for post-treatment ATT(g,t); pre-treatment diagnostics use a fixed baseline and may differ from CS's default varying baseline\n4. The efficiency gain comes from optimally weighting across all valid (comparison group, baseline) pairs\n5. **Event study** and **group** aggregations work just like CS\n6. **Multiplier bootstrap** provides robust inference with Rademacher, Mammen, or Webb weights\n7. **Condition numbers** flag potentially unstable weight matrices\n8. **Anticipation** shifts the effective treatment boundary for pre-treatment effects\n9. Phase 1 is **no-covariates only** --- Phase 2 will add covariate support\n10. When in doubt, run both EDiD and CS --- if ATTs agree, report EDiD for tighter CIs\n\n**Parameter reference:**\n\n| Parameter | Default | Description |\n|-----------|---------|-------------|\n| `pt_assumption` | `\"all\"` | `\"all\"` (overidentified) or `\"post\"` (just-identified, matches CS post-treatment ATT) |\n| `alpha` | `0.05` | Significance level |\n| `n_bootstrap` | `0` | Number of bootstrap iterations (0 = analytical only) |\n| `bootstrap_weights` | `\"rademacher\"` | Bootstrap weight distribution: `\"rademacher\"`, `\"mammen\"`, `\"webb\"` |\n| `seed` | `None` | Random seed for reproducibility |\n| `anticipation` | `0` | Anticipation periods |\n\n**Reference:** Chen, X., Sant'Anna, P. H. C., & Xie, H. (2025). Efficient Difference-in-Differences and Event Study Estimators.\n\n*See also: [Choosing an Estimator](../choosing_estimator.rst) for guidance on when to use EDiD vs other estimators.*" |
503 | 489 | } |
504 | 490 | ], |
505 | 491 | "metadata": { |
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