causal-inference

Files (4)

• SKILL.md
• method-implementations.md · references/
• staggered-did.md · references/
• synthetic-control.md · references/

SKILL.md (first lines)

# Causal Inference

Reference for implementing causal inference methods: from identification strategy to estimation to diagnostics and robustness. Covers the major quasi-experimental and observational methods used in applied economics and quantitative social science.

## When to Use This Skill

Use when the user is:
- Choosing an identification strategy for a causal question
- Implementing IV/2SLS, DiD, RDD, synthetic control, or matching
- Debugging specification issues (weak instruments, parallel trends violations, bandwidth sensitivity)
- Running robustness checks or falsification tests
- Working with modern DiD methods for staggered treatment timing

Skip when:
- The task is structural estimation (use `structural-modeling` skill)
- The task is pure prediction/ML (no causal question)
- The user needs simulation design (use `numerical-auditor` agent)

## Where to Start
- **Choosing a method?** Jump to [Method Selection Guide](#method-selection-guide) at the end
- **Implementing a specific method?** Go directly to that method's section below
- **Need full code?** See `references/method-implementations.md` for complete implementations

## Frameworks

Two complementary frameworks underpin all causal inference:

**Potential Outcomes (Rubin):** Define Y(1), Y(0) as potential outcomes under treatment and control. The causal effect is τ = Y(1) - Y(0). The fundamental problem: we never observe both for the same unit. All methods are strategies for constructing valid counterfactuals.

**DAGs (Pearl):** Graphical models encoding conditional independence assumptions. Use d-separation to determine what must be conditioned on (and what must NOT be conditioned on) to identify causal effects. Particularly useful for reasoning about bad controls (colliders, mediators), overcontrol bias, and which instruments satisfy the exclusion restriction.

## Quick Reference: Methods at a Glance

| Method | Key Assumption | Target Parameter | Key Package |
|--------|---------------|-----------------|-------------|
| IV/2SLS | Exclusion restriction, monotonicity | LATE | `linearmodels` (Py), `fixest` (R), `ivregress` (Stata) |
| DiD | Parallel trends | ATT | `fixest` (R), `reghdfe` (Stata), `linearmodels` (Py) |
| RDD | No manipulation, local continuity | LATE at cutoff | `rdrobust` (all) |
| Synthetic Control | Weights reproduce pre-treatment trends | ATT (single unit) | `Synth`/`augsynth` (R) |
| Matching/AIPW | Selection on observables | ATE or ATT | `econml` (Py), `MatchIt`/`WeightIt` (R) |

## Target Parameters

Be precise about what parameter you are estimating:

| Parameter | Definition | Estimated by |
|-----------|-----------|-------------|
| ATE | E[Y(1) - Y(0)] | Randomized experiment, IPW, AIPW |
| ATT | E[Y(1) - Y(0) \| D=1] | DiD, matching, selection-on-observables |
| LATE | E[Y(1) - Y(0) \| compliers] | IV/2SLS (Imbens-Angrist 1994) |
| ATT(g,t) | Group-time specific treatment effect | Staggered DiD (Callaway-Sant'Anna) |

**Common mistake:** IV estimates LATE, not ATE. DiD estimates ATT, not ATE. This matters for policy interpretation.

## Instrumental Variables (IV/2SLS)

**Key idea:** Find a variable Z that shifts D (first stage) but affects Y only through D (exclusion restriction).

```python
from linearmodels.iv import IV2SLS

result = IV2SLS.from_formula(
    'lwage ~ 1 + exper + expersq + [educ ~ nearc4 + nearc2]',
    data=df
).fit(cov_type='robust')

# Always check first-stage F > 10; report LIML as robustness with weak instruments
```

For R/Stata implementations, weak instrument corrections (LIML, Anderson-Rubin), and overidentification tests, see `references/method-implementations.md`.

**IV Diagnostics Checklist:**
- [ ] First-stage F > 10 (or Olea-Pflueger effective F for robust inference)
- [ ] Exclusion restriction argued substantively (not testable)
- [ ] Monotonicity for LATE interpretation (no defiers)
- [ ] Reduced form significant (regress Y directly on Z)
- [ ] Overidentification test reported if over-identified
- [ ] Compare OLS vs 2SLS — direction and magnitude as expected?
- [ ] Report LATE interpretation — who are the compliers?

## Difference-in-Differences (DiD)

**Key idea:** Compare changes over time between treated and control groups, assuming they would have followed parallel trends absent treatment.

```python
import statsmodels.formula.api as smf

# Standard 2x2 DiD
result = smf.ols('y ~ treated + post + treated:post', data=df).fit(
    cov_type='cluster', cov_kwds={'groups': df['state']}
)
# Coefficient on treated:post is the DiD estimate
```

**Staggered treatment timing:** With staggered adoption, TWFE can produce sign-reversed estimates due to negative weights. Use:
- **Callaway-Sant'Anna** (`did` R package): Most flexible aggregation, doubly robust
- **Sun-Abraham** (`fixest::sunab`): Integrates directly into `feols`; simpler for event studies
- **Bacon decomposition** (`bacondecomp` R): Diagnose how much weight TWFE puts on contaminated comparisons

For full staggered DiD code (C-SA, Sun-Abraham, BJS24, de Chaisemartin-D'H), see `references/staggered-did.md`. For event study code and HonestDiD pre-trend sensitivity, see `references/method-implementations.md`.

**DiD Diagnostics Checklist:**
- [ ] Pre-trends: Event study shows no significant pre-treatment coefficients
- [ ] Parallel trends sensitivity: Rambachan-Roth or similar analysis
- [ ] Staggered timing: If varies, use C-SA or S-A — NOT naive TWFE
- [ ] Clustering at level of treatment assignment (typically state/county)
- [ ] Anticipation: Check period just before treatment
- [ ] Bacon decomposition if using TWFE

## Regression Discontinuity (RDD)

**Key idea:** Units just above and below a threshold are locally comparable; the jump at the threshold identifies the causal effect.

```python
from rdrobust import rdrobust, rdbwselect, rdplot

# Basic sharp RD with bias-corrected robust CI
result = rdrobust(y=df['outcome'], x=df['running_var'], c=0)
# Reports: point estimate, robust CI, MSE-optimal bandwidth, N left/right

From James-Traina/compound-science, MIT.