Instrumental Variables Analysis AI Prompt

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.