Causal Inference AI Prompts

Design and analyze a difference-in-differences (DiD) study to estimate a causal effect from panel data. Treatment: {{treatment}} (a policy, intervention, or event that affects some units but not others) Timing: {{timing}} (when did the treatment occur?) Panel data: {{data_description}} (units observed before and after the treatment) Comparison groups: {{treatment_group}} (treated) vs {{control_group}} (untreated) 1. DiD logic: DiD = (Mean_treated_post - Mean_treated_pre) - (Mean_control_post - Mean_control_pre) The control group's change over time is used to estimate the counterfactual trend for the treated group. The key identifying assumption is parallel trends: absent the treatment, treated and control units would have evolved in parallel. 2. Parallel trends assumption: - Check pre-treatment trends: plot the outcome for treated and control groups across all pre-treatment periods - If trends are parallel pre-treatment: assumption is plausible (not proven) - Formal test: interact treatment group with pre-treatment time dummies; if coefficients are jointly zero, trends are parallel - Event study plot: plot the treatment effect coefficient for each period relative to treatment, including pre-treatment leads. Pre-treatment coefficients should be near zero. 3. DiD regression specification: y_it = alpha + beta1 Treated_i + beta2 Post_t + delta (Treated_i x Post_t) + epsilon_it - delta is the DiD estimator - Add unit fixed effects (absorbs all time-invariant unit characteristics) - Add time fixed effects (absorbs common shocks) - Two-way fixed effects (TWFE): y_it = alpha_i + alpha_t + delta D_it + epsilon_it where D_it = 1 if unit i is treated in period t 4. Staggered treatment timing: - If different units receive treatment at different times, TWFE can be biased - Modern estimators for staggered DiD: Callaway-Sant'Anna, Sun-Abraham, de Chaisemartin-d'Haultfoeuille - These estimators form clean 2x2 DiD comparisons and average them correctly - Use the csdid (Stata) or did (R) package 5. Standard errors: - Cluster standard errors at the unit level (accounts for serial correlation within units) - If few treated clusters (< 10): wild cluster bootstrap for valid inference - Placebo tests: apply DiD to a period before treatment; the estimated effect should be near zero Return: DiD estimate, parallel trends test, event study plot description, staggered timing assessment, and clustered SE specification.

Specify and implement an instrumental variables (IV) analysis to estimate a causal effect in the presence of unmeasured confounding. Exposure (endogenous treatment): {{treatment}} Outcome: {{outcome}} Proposed instrument: {{instrument}} Data: {{data_description}} 1. What IV analysis does: IV exploits an external source of variation (the instrument) that affects the treatment but does NOT directly affect the outcome except through the treatment. It can identify a causal effect even when there are unmeasured confounders. The causal estimate is the LATE: Local Average Treatment Effect — the effect for 'compliers' (those whose treatment status is changed by the instrument). 2. Three conditions for a valid instrument: Relevance: - The instrument Z must be associated with the treatment X - Testable: regress X on Z; the F-statistic for Z should be > 10 (rule of thumb for weak instruments) - Weak instrument problem: if F < 10, IV estimates are biased toward OLS and SEs are inflated Independence (Exogeneity): - Z must be independent of unmeasured confounders U - Not directly testable: requires a substantive argument - Examples of plausible instruments: geographic variation in access, distance to a facility, lottery assignment, policy cutoffs, genetic variants (Mendelian randomization) Exclusion restriction: - Z affects Y ONLY through X (no direct effect of Z on Y) - Not directly testable: requires a substantive argument - Violations: instrument affects outcome through other pathways (e.g., distance to a hospital affects health through access AND through living in a different environment) 3. Two-stage least squares (2SLS): Stage 1: X_hat = alpha + beta_1 Z + covariates Stage 2: Y = gamma + delta X_hat + covariates IV estimate delta = Cov(Z, Y) / Cov(Z, X) In practice: use ivreg() in R or ivregress in Stata/Python (do not manually run 2SLS in two steps — standard errors will be wrong). 4. Diagnostics: - First-stage F-statistic: test instrument relevance (target > 10, prefer > 16 for reliable inference) - Sargan-Hansen test: overidentification test if multiple instruments (test exclusion restriction) - Anderson-Rubin test: robust inference under weak instruments 5. Interpretation and limitations: - IV estimates are typically larger than OLS (because IV estimates a local effect for compliers, who may respond more strongly) - Large IV SEs: IV is less efficient than OLS when instrument is only moderately relevant - The LATE may not generalize to the full population (only compliers) Return: instrument validity assessment, 2SLS specification, first-stage F-statistic, IV estimate with CI, and interpretation of LATE.

Implement and evaluate a propensity score analysis to estimate a causal effect from observational data. Treatment variable: {{treatment}} (binary: treated vs untreated) Outcome: {{outcome}} Potential confounders: {{confounders}} Data: {{data_description}} 1. Estimand clarification: - ATE (Average Treatment Effect): the effect if the entire population were treated vs untreated - ATT (Average Treatment Effect on the Treated): the effect for those who actually received treatment - ATC: average effect for the controls if they had been treated - Choose based on the scientific question; ATT is most common in observational studies 2. Propensity score estimation: PS = P(Treatment = 1 | X) - Fit a logistic regression with treatment as the outcome and all confounders as predictors - Include: all variables that affect the outcome OR that affect both treatment and outcome - Do NOT include: instrumental variables (variables affecting treatment but NOT outcome) - Do NOT include: colliders (effects of treatment or outcome) - Check common support: there should be overlap in PS distributions between treated and controls Limited overlap = inability to estimate causal effect for some subgroups 3. PS matching: - Nearest neighbor matching: each treated unit matched to the closest control by PS - Caliper matching: require |PS_treated - PS_control| < 0.2 x SD(PS) (discard poor matches) - 1:1 vs 1:k matching: k>1 increases precision but introduces bias if poor matches are forced - Matching with replacement: allows controls to be reused (reduces bias, increases variance) 4. Balance assessment: - Standardized mean differences (SMD) before and after matching for each confounder - SMD < 0.10 after matching: good balance - Love plot: visualize SMD for each confounder before and after adjustment - Do NOT use p-values for balance checking — they are affected by sample size, not balance 5. Analysis after matching: - Estimate the treatment effect using a paired or stratified outcome model - Use doubly robust estimation: combine PS weighting with outcome regression (consistent if either is correct) - Report: estimated causal effect, 95% CI (using robust standard errors), and the matched sample size 6. Sensitivity analysis for unmeasured confounding: - Rosenbaum bounds: how strong would an unmeasured confounder need to be to explain away the result? - Gamma parameter: if Gamma = 2, the odds of treatment could differ by a factor of 2 for matched pairs with identical observed covariates - E-value: minimum association a confounder would need with both treatment and outcome to fully explain the observed effect Return: PS model specification, overlap assessment, balance table (pre/post), causal effect estimate, and sensitivity analysis.