grad-did
用雙重差分法比較處理組和對照組，估計政策的因果效果
中文翻譯
--- name: "grad-did" description: "用雙重差分法（DID）比較處理組與對照組的結果變化，估計因果處理效果。當使用者要評估政策介入、自然實驗或法規變動、需要檢定平行趨勢，或問到「這個政策有沒有用」「沒有隨機分派要怎麼識別因果效果」「處理效果是多少」時，就用這個 skill。" metadata: category: "WP-31 量化方法" tags: ["DID", "difference-in-differences", "causal-inference", "parallel-trends", "policy-evaluation", "treatment-effect"] --- # 雙重差分法 (Difference-in-Differences) ## Overview 雙重差分法（DID）比較處理組（受介入影響）和對照組（不受影響）在一段時間內的結果變化，藉此估計因果效果。它同時扣掉不隨時間變動的組間差異，以及共同的時間趨勢，所以在平行趨勢假設下，可以把處理效果單獨分離出來。 ## When to Use - 評估政策、法規或介入措施的影響 - 自然實驗在群體層級（州、產業、公司）分派處理 - 有處理前後期間的 panel 或重複橫斷面資料 - 無法做隨機實驗，但存在合理的對照組 ## When NOT to Use - 平行趨勢假設被違反，而且無法補救 - 處理組和對照組的差異會隨時間改變 - 處理是根據預期結果自我選擇的（預期效應） - 只有處理後的資料（沒有處理前的基準） ## Assumptions ``` IRON LAW: DID is valid ONLY if the parallel trends assumption holds — without it, the estimated treatment effect is biased by differential pre-existing trends. ``` 關鍵假設： 1. 平行趨勢：沒有處理的話，處理組和對照組會沿著相同的軌跡走 2. 處理單位不會對對照單位產生外溢效應（SUTVA） 3. 處理時點明確且外生 4. 各組的組成隨時間穩定（沒有差別性的流失） ## Methodology ### Step 1 — Establish Treatment and Control Groups 定義誰被處理、什麼時候被處理。驗證兩組在處理前的可觀察特徵上是可比較的。記錄處理事件與其時點。 ### Step 2 — Test Parallel Trends 畫出處理組與對照組在處理前期間的結果趨勢。跑一個含 leads 和 lags 的 event-study 設定。處理前的係數在統計上應該不顯著。 ### Step 3 — Estimate the DID Model Y = β₀ + β₁×Treat + β₂×Post + β₃×(Treat×Post) + Controls + ε。係數 β₃ 就是 DID 估計量。標準誤要在處理分派的層級做 cluster。交錯採用（staggered adoption）的延伸見 `references/`。 ### Step 4 — Robustness Checks 跑安慰劑檢定（假的處理日期、假的處理組）。測試結果對對照組選擇的敏感度。交錯 DID 要用 Callaway-Sant'Anna 或 Sun-Abraham 估計量。 ## Output Format ```markdown ## DID Analysis: [Policy / Intervention] ### Research Design | Element | Description | |---------|-------------| | Treatment group | [who] | | Control group | [who] | | Treatment date | [when] | | Pre-treatment periods | [range] | ### Parallel Trends Test | Pre-period lead | Coefficient | S.E. | p-value | |-----------------|-------------|------|---------| | t-3 | x.xx | x.xx | x.xx | | t-2 | x.xx | x.xx | x.xx | | t-1 | x.xx | x.xx | x.xx | ### DID Estimate | Specification | β (Treat×Post) | S.E. | p-value | N | |---------------|----------------|------|---------|---| | Baseline | x.xx | x.xx | x.xx | xxx | | With controls | x.xx | x.xx | x.xx | xxx | ### Robustness - Placebo test result: [pass/fail] - Alternative control group: [result] ### Limitations - [Note any assumption violations] ``` ## Gotchas - 目視平行趨勢是必要條件，不是充分條件，因為這個假設講的是反事實的趨勢 - cluster 太少時，對標準誤做 cluster 會膨脹第一型錯誤（cluster < 50 時用 wild bootstrap） - 交錯採用會讓標準的雙向固定效果 DID 估計量產生偏誤（改用近期發展的穩健估計量） - 預期效應違反了處理時點明確的假設 - 處理前趨勢不同，常用加入組別專屬趨勢來「修正」，但這很脆弱 - DID 估計的是對受處理者的局部平均處理效果（ATT），不是 ATE ## References - Angrist, J. D., & Pischke, J.-S. (2009). *Mostly Harmless Econometrics*. Princeton University Press. - Callaway, B., & Sant'Anna, P. H. C. (2021). Difference-in-differences with multiple time periods. *Journal of Econometrics*, 225(2), 200-230. - Goodman-Bacon, A. (2021). Difference-in-differences with variation in treatment timing. *Journal of Econometrics*, 225(2), 254-277.
英文原文
--- name: "grad-did" description: "Apply Difference-in-Differences (DID) to estimate causal treatment effects by comparing changes in outcomes between treatment and control groups. Use this skill when the user evaluates policy interventions, natural experiments, or regulatory changes, needs to test parallel trends, or when they ask 'did this policy work', 'how do I identify causal effects without randomization', or 'what is the treatment effect'." metadata: category: "WP-31 量化方法" tags: ["DID", "difference-in-differences", "causal-inference", "parallel-trends", "policy-evaluation", "treatment-effect"] --- # 雙重差分法 (Difference-in-Differences) ## Overview Difference-in-Differences (DID) estimates causal effects by comparing the change in outcomes over time between a treatment group (affected by an intervention) and a control group (unaffected). By differencing out both time-invariant group differences and common time trends, DID isolates the treatment effect under the parallel trends assumption. ## When to Use - Evaluating the impact of a policy, regulation, or intervention - A natural experiment assigns treatment at a group level (state, industry, firm) - Panel or repeated cross-section data with pre- and post-treatment periods - Randomized experiment is infeasible but a plausible control group exists ## When NOT to Use - Parallel trends assumption is violated and cannot be remedied - Treatment and control groups differ in ways that change over time - Treatment is self-selected based on anticipated outcomes (anticipation effects) - Only post-treatment data are available (no pre-treatment baseline) ## Assumptions ``` IRON LAW: DID is valid ONLY if the parallel trends assumption holds — without it, the estimated treatment effect is biased by differential pre-existing trends. ``` Key assumptions: 1. Parallel trends: absent treatment, treated and control groups would have followed the same trajectory 2. No spillover effects from treated to control units (SUTVA) 3. Treatment timing is sharp and exogenous 4. Composition of groups is stable over time (no differential attrition) ## Methodology ### Step 1 — Establish Treatment and Control Groups Define who is treated and when. Verify groups are comparable on pre-treatment observables. Document the treatment event and its timing. ### Step 2 — Test Parallel Trends Plot outcome trends for treatment vs control groups in pre-treatment periods. Run an event-study specification with leads and lags. Pre-treatment coefficients should be statistically insignificant. ### Step 3 — Estimate the DID Model Y = β₀ + β₁×Treat + β₂×Post + β₃×(Treat×Post) + Controls + ε. The coefficient β₃ is the DID estimator. Cluster standard errors at the treatment assignment level. See `references/` for staggered adoption extensions. ### Step 4 — Robustness Checks Run placebo tests (fake treatment dates, fake treatment groups). Test sensitivity to control group choice. For staggered DID, use Callaway-Sant'Anna or Sun-Abraham estimators. ## Output Format ```markdown ## DID Analysis: [Policy / Intervention] ### Research Design | Element | Description | |---------|-------------| | Treatment group | [who] | | Control group | [who] | | Treatment date | [when] | | Pre-treatment periods | [range] | ### Parallel Trends Test | Pre-period lead | Coefficient | S.E. | p-value | |-----------------|-------------|------|---------| | t-3 | x.xx | x.xx | x.xx | | t-2 | x.xx | x.xx | x.xx | | t-1 | x.xx | x.xx | x.xx | ### DID Estimate | Specification | β (Treat×Post) | S.E. | p-value | N | |---------------|----------------|------|---------|---| | Baseline | x.xx | x.xx | x.xx | xxx | | With controls | x.xx | x.xx | x.xx | xxx | ### Robustness - Placebo test result: [pass/fail] - Alternative control group: [result] ### Limitations - [Note any assumption violations] ``` ## Gotchas - Visual parallel trends are necessary but not sufficient — the assumption is about counterfactual trends - Too few clusters for clustering standard errors inflates Type I error (use wild bootstrap if clusters < 50) - Staggered adoption makes the standard two-way FE DID estimator biased (use recent robust estimators) - Anticipation effects violate the sharp treatment timing assumption - Differential pre-trends are often "fixed" by adding group-specific trends, but this is fragile - DID estimates a local average treatment effect on the treated (ATT), not ATE ## References - Angrist, J. D., & Pischke, J.-S. (2009). *Mostly Harmless Econometrics*. Princeton University Press. - Callaway, B., & Sant'Anna, P. H. C. (2021). Difference-in-differences with multiple time periods. *Journal of Econometrics*, 225(2), 200-230. - Goodman-Bacon, A. (2021). Difference-in-differences with variation in treatment timing. *Journal of Econometrics*, 225(2), 254-277.