j4flmao Causal Inference
Purpose
Estimate causal effects from observational and experimental data using rigorous frameworks and methods: causal frameworks (potential outcomes / Rubin Causal Model, directed acyclic graphs / Pearl's framework, do-calculus, counterfactual reasoning, structural causal models), quasi-experimental methods (difference-in-differences, regression discontinuity design, instrumental variables, propensity score matching, synthetic control), and causal machine learning (uplift modeling, heterogeneous treatment effects, CATE estimation, S/T/X-learners, causal forests, double/debiased ML).
Agent Protocol
Trigger
Exact user phrases: "causal inference", "causal effect", "treatment effect", "potential outcomes", "Rubin causal model", "DAG", "directed acyclic graph", "do-calculus", "counterfactual", "structural causal model", "SCM", "difference-in-differences", "DiD", "regression discontinuity", "RDD", "instrumental variable", "IV", "propensity score", "PSM", "synthetic control", "uplift modeling", "heterogeneous treatment effect", "HTE", "CATE", "conditional average treatment effect", "meta-learner", "S-learner", "T-learner", "X-learner", "causal forest", "double ML", "debiased ML", "confounding", "selection bias", "endogeneity", "identification".
Input Context
Before activating, verify:
- Data source (RCT, observational, panel, time series)
- Treatment assignment mechanism (random, conditional, self-selection)
- Confounders observed and unobserved
- Target estimand (ATE, ATT, CATE, ITE)
- Domain knowledge for DAG construction
- Sample size and dimensionality
- Budget/computational constraints for causal ML
Output Artifact
Causal analysis plan with identification strategy, estimation method, robustness checks, and sensitivity analysis.
Response Format
# Estimation code
# CATE estimates: ATE, ATT, heterogeneity analysis
# DAG specification in DOT notation
# Sensitivity analysis results
No preamble. No postamble. No explanations. No filler/hedging/transitions. Compress output — why use many token when few do trick.
Completion Criteria
- Causal question formalized with treatment, outcome, and confounders
- DAG constructed and identification strategy justified
- Estimand clearly defined (ATE, ATT, CATE, LATE)
- Estimation method chosen with assumptions stated
- Robustness checks (placebo, permutation, sensitivity)
- Results reported with confidence intervals and interpretation
- Limitations and untestable assumptions documented
Max Response Length
400 lines of code and output.
Workflow
Step 1: Causal Graph Specification
# DAG specification with DOT notation
dag_spec = """
digraph CausalModel {
Z [label="Instrument Z"]
X [label="Treatment X"]
Y [label="Outcome Y"]
C1 [label="Confounder C1"]
C2 [label="Confounder C2"]
C1 -> X; C1 -> Y
C2 -> X; C2 -> Y
X -> Y
Z -> X
}
"""
import networkx as nx
from causallearn.graph import GeneralGraph
from causallearn.utils.cit import chisq, fisherz
def dag_backdoor_criteria(graph, treatment, outcome):
"""Check if backdoor criterion is satisfied."""
ancestors_t = nx.ancestors(graph, treatment)
ancestors_o = nx.ancestors(graph, outcome)
# Nodes on backdoor paths (non-causal paths from treatment to outcome)
backdoor_set = set()
for node in graph.nodes:
paths = list(nx.all_simple_paths(graph, treatment, outcome))
for path in paths:
if node in path[1:-1]:
backdoor_set.add(node)
return backdoor_set
Step 2: Propensity Score Methods
from sklearn.linear_model import LogisticRegression
import numpy as np
def propensity_score(X, t):
model = LogisticRegression(max_iter=1000, penalty=None)
model.fit(X, t)
return model.predict_proba(X)[:, 1]
def ipw_estimate(y, t, ps):
"""Inverse probability weighting for ATE."""
weights = t / ps + (1 - t) / (1 - ps)
ate = np.mean(t * y / ps - (1 - t) * y / (1 - ps))
# Stabilized weights
p_t = np.mean(t)
sw = t * p_t / ps + (1 - t) * (1 - p_t) / (1 - ps)
ate_stable = np.mean(t * y / ps * p_t - (1 - t) * y / (1 - ps) * (1 - p_t))
return {"ate": ate, "ate_stabilized": ate_stable, "weights": weights}
def matching_estimator(y, t, X, caliper=0.05):
"""Nearest neighbor matching with caliper."""
from sklearn.neighbors import NearestNeighbors
treated = X[t == 1]
control = X[t == 0]
nn = NearestNeighbors(n_neighbors=1, metric="euclidean")
nn.fit(control)
distances, indices = nn.kneighbors(treated)
valid = distances.flatten() < caliper
matched_control = control[indices[valid].flatten()]
att = np.mean(y[t == 1][valid]) - np.mean(y[t == 0][indices[valid].flatten()])
return {"att": att, "n_matched": np.sum(valid), "n_unmatched": np.sum(~valid)}
Step 3: Difference-in-Differences
import statsmodels.api as sm
def did_estimation(df, outcome, treatment, post, unit_fe, time_fe):
"""Two-way fixed effects DiD."""
df["did"] = df[treatment] * df[post]
X = df[["did", treatment, post]]
X = sm.add_constant(X)
y = df[outcome]
model = sm.OLS(y, X).fit()
return {
"did_coef": model.params["did"],
"ci": model.conf_int().loc["did"].tolist(),
"p_value": model.pvalues["did"]
}
def event_study(df, outcome, treatment, event_time, unit_fe, time_fe, leads=5, lags=5):
"""Event study with leads and lags."""
import patsy
from statsmodels.regression.linear_model import OLS
for lag in range(-leads, lags + 1):
if lag == -1:
continue
df[f"event_{lag}"] = (df[treatment] & (df[event_time] == lag)).astype(int)
formula = f"{outcome} ~ " + " + ".join([f"event_{lag}" for lag in range(-leads, lags + 1) if lag != -1]) + f" + C({unit_fe}) + C({time_fe})"
y, X = patsy.dmatrices(formula, df, return_type="dataframe")
model = OLS(y, X).fit()
return model
Step 4: Regression Discontinuity
def rdd_estimation(df, outcome, running_var, cutoff, bandwidth=None, order=2):
"""Sharp RDD with local polynomial regression."""
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
if bandwidth is None:
bandwidth = np.std(df[running_var]) * 0.5
df_rdd = df[(df[running_var] >= cutoff - bandwidth) & (df[running_var] <= cutoff + bandwidth)].copy()
df_rdd["treatment"] = (df_rdd[running_var] >= cutoff).astype(float)
df_rdd["running_centered"] = df_rdd[running_var] - cutoff
poly = PolynomialFeatures(degree=order, interaction_only=False, include_bias=False)
X_base = df_rdd[["running_centered"]].values
X_poly = poly.fit_transform(X_base)
X = np.column_stack([df_rdd["treatment"].values, X_poly])
model = LinearRegression().fit(X, df_rdd[outcome])
return {"lwald_estimate": model.coef_[0], "bandwidth": bandwidth, "n": len(df_rdd)}
Step 5: Instrumental Variables
def iv_2sls(y, t, X, instrument):
"""Two-stage least squares."""
import statsmodels.api as sm
# First stage: regress treatment on instrument
Z = sm.add_constant(np.column_stack([instrument, X]))
first_stage = sm.OLS(t, Z).fit()
t_hat = first_stage.fittedvalues
# Second stage: regress outcome on predicted treatment
W = sm.add_constant(np.column_stack([t_hat, X]))
second_stage = sm.OLS(y, W).fit()
return {
"coef": second_stage.params[1],
"ci": second_stage.conf_int().loc[W.columns[1]].tolist(),
"p_value": second_stage.pvalues[1],
"first_stage_f": first_stage.fvalue,
"weak_instrument": first_stage.fvalue < 10
}
Step 6: Causal ML — Meta-Learners
from sklearn.ensemble import GradientBoostingRegressor, RandomForestRegressor
from sklearn.linear_model import LogisticRegression
def s_learner(X, y, t):
"""Single model: include treatment as feature."""
model = GradientBoostingRegressor(n_estimators=100)
X_with_t = np.column_stack([X, t])
model.fit(X_with_t, y)
X1 = np.column_stack([X, np.ones(len(X))])
X0 = np.column_stack([X, np.zeros(len(X))])
cate = model.predict(X1) - model.predict(X0)
return {"model": model, "cate_mean": np.mean(cate), "cate_std": np.std(cate)}
def t_learner(X, y, t):
"""Two models: separate models for treated and control."""
model_t = GradientBoostingRegressor(n_estimators=100)
model_c = GradientBoostingRegressor(n_estimators=100)
model_t.fit(X[t == 1], y[t == 1])
model_c.fit(X[t == 0], y[t == 0])
cate = model_t.predict(X) - model_c.predict(X)
return {"model_t": model_t, "model_c": model_c, "cate_mean": np.mean(cate), "cate_std": np.std(cate)}
def x_learner(X, y, t):
"""X-learner: cross-learn propensity and treatment effects."""
# Propensity model
ps_model = LogisticRegression().fit(X, t)
ps = ps_model.predict_proba(X)[:, 1]
# Impute treatment effects
model_t = GradientBoostingRegressor().fit(X[t == 1], y[t == 1])
model_c = GradientBoostingRegressor().fit(X[t == 0], y[t == 0])
d_t = y[t == 1] - model_c.predict(X[t == 1])
d_c = model_t.predict(X[t == 0]) - y[t == 0]
# Weight by propensity
model_d_t = GradientBoostingRegressor().fit(X[t == 1], d_t)
model_d_c = GradientBoostingRegressor().fit(X[t == 0], d_c)
tau_t = model_d_t.predict(X)
tau_c = model_d_c.predict(X)
cate = ps * tau_t + (1 - ps) * tau_c
return {"cate_mean": np.mean(cate), "cate_std": np.std(cate)}
Step 7: Causal Forests
from econml.grf import CausalForest
def causal_forest_ate(X, y, t):
cf = CausalForest(n_estimators=500, min_samples_leaf=10, max_depth=20)
cf.fit(X, t, y)
ate = cf.marginal_effect(X).mean()
te = cf.marginal_effect(X)
return {"ate": ate[0], "cate_stderr": te.std(), "model": cf}
def heterogeneous_effects(cf, X, feature_names=None):
te = cf.marginal_effect(X)
# Variable importance for heterogeneity
imp = cf.feature_importances_
return {"treatment_effects": te, "importance": dict(zip(feature_names or range(len(imp)), imp))}
Step 8: Double/Debiased ML
from econml.dml import LinearDML
def double_ml(X, y, t, model_y=None, model_t=None):
if model_y is None:
model_y = GradientBoostingRegressor(n_estimators=100, max_depth=3)
if model_t is None:
model_t = LogisticRegression(max_iter=1000)
dml = LinearDML(model_y=model_y, model_t=model_t, discrete_treatment=True)
dml.fit(y, t, X=X)
ate = dml.ate()
ci = dml.ate_interval()
return {"ate": ate, "ci_95": ci}
Method Comparison
method_selection:
randomized_experiment:
assumptions: "Randomization, no spillover, compliance"
estimand: "ATE, ATT, CATE"
data_required: "RCT design, outcome + treatment"
strength: "Gold standard — unbiased if randomization holds"
weakness: "Expensive, not always feasible, external validity concerns"
difference_in_differences:
assumptions: "Parallel trends, no spillover, common shocks"
estimand: "ATT (treated vs control over time)"
data_required: "Panel data with pre/post periods + untreated control"
strength: "Controls for time-invariant confounders"
weakness: "Parallel trends assumption untestable; sensitive to time window"
regression_discontinuity:
assumptions: "Continuity at cutoff, no manipulation of running variable"
estimand: "LATE at cutoff"
data_required: "Running variable with threshold, outcome"
strength: "Credible near cutoff (gold standard for local effects)"
weakness: "Low external validity, requires large N near cutoff, limited power"
instrumental_variables:
assumptions: "Relevance, exclusion, exchangeability"
estimand: "LATE (compliers)"
data_required: "Valid instrument, outcome, treatment"
strength: "Handles unobserved confounders if valid instrument exists"
weakness: "Strong instruments are rare; weak instrument bias; LATE interpretation"
propensity_score_matching:
assumptions: "Ignorability (unconfoundedness), overlap, SUTVA"
estimand: "ATE or ATT (with matching)"
data_required: "Observational data with all confounders measured"
strength: "Intuitive, mimics RCT design"
weakness: "Only measured confounders; sensitivity to matching method"
synthetic_control:
assumptions: "Pre-treatment fit, no interference, convex combination"
estimand: "ATT (single treated unit)"
data_required: "Panel data, single treated unit, multiple control units"
strength: "Transparent weights, data-driven control construction"
weakness: "Only for single treated unit; extrapolation concerns"
double_ML:
assumptions: "Ignorability, overlap, Neyman orthogonality"
estimand: "ATE, CATE"
data_required: "Observational data with high-dimensional confounders"
strength: "Handles high-dimensional confounders, robust to model misspecification"
weakness: "Requires sample splitting; sensitive to ML model choices"
Sensitivity Analysis
# E-value: how strong must an unobserved confounder be to explain away the effect?
# E-value = RR + sqrt(RR × (RR - 1)) for RR > 1
def e_value(estimate, lower_ci=None, upper_ci=None):
"""
Compute E-value for a risk ratio estimate.
Minimum strength of association an unobserved confounder
must have with BOTH treatment and outcome to explain away the effect.
"""
def compute_eval(rr):
if rr <= 1:
return 1.0
return rr + np.sqrt(rr * (rr - 1))
eval_est = compute_eval(estimate)
eval_ci = None
if lower_ci is not None and upper_ci is not None:
# Use CI closest to null
ci_closest = max(min(upper_ci, 1/upper_ci), lower_ci)
if ci_closest >= 1:
eval_ci = compute_eval(ci_closest)
else:
eval_ci = 1.0
return {"e_value_estimate": eval_est, "e_value_ci": eval_ci}
# Example: RR = 2.0, 95% CI [1.5, 2.5]
# E-value for estimate: 3.41
# Interpretation: unobserved confounder must be associated with
# both treatment and outcome by RR of 3.41+ to explain away the effect
Common Causal Pitfalls
pitfalls:
- name: "Collider bias (Berkson's paradox)"
description: "Stratifying on a collider opens a non-causal path between treatment and outcome"
example: "Analyzing hospital patients: sicker patients get more treatment, but also have worse outcomes"
fix: "Do NOT condition on colliders; use DAG to identify colliders before adjustment set selection"
- name: "M-bias"
description: "A collider between two confounders, conditioning on it creates bias"
example: "X ← U1 → C ← U2 → Y, conditioning on C creates non-causal X-Y association"
fix: "Use backdoor criterion; only condition on non-colliders that block backdoor paths"
- name: "Over-adjustment (controlling for mediators)"
description: "Conditioning on a variable on the causal path from treatment to outcome"
example: "Treatment affects learning, which affects score. Controlling for learning attenuates effect"
fix: "Do NOT condition on mediators unless estimating direct effect (different estimand)"
- name: "Post-treatment selection bias"
description: "Conditioning on an outcome that happens after treatment, confounded by both"
example: "Only analyzing users who completed a tutorial (affected by treatment)"
fix: "Use intention-to-treat analysis; handle attrition via bounds or inverse probability weighting"
- name: "Weak instrument bias"
description: "IV with weak correlation to treatment produces biased estimates even in large samples"
example: "Using lottery wins as instrument for education — weak when few people win"
fix: "Check F-statistic > 10 for first stage; use robust IV methods (LIML, jackknife IV)"
- name: "Look-ahead bias (anticipation effects)"
description: "Units change behavior in anticipation of treatment"
example: "Companies adjust inventory before a tariff announcement takes effect"
fix: "Use announcement date not effective date; placebo tests on pre-treatment periods"
Causal Discovery
# Causal structure learning (for hypothesis generation, not confirmation)
from causallearn.search.ConstraintBased.PC import pc
from causallearn.utils.GraphUtils import GraphUtils
def learn_dag(data, alpha=0.05, independence_test='fisherz'):
"""
PC algorithm for causal discovery.
WARNING: outputs causal graph, NOT causal effects.
Use for DAG hypothesis generation, then validate with domain experts.
"""
cg = pc(data, alpha=alpha, indep_test=independence_test)
# Convert to DOT for visualization
pyd = GraphUtils.to_pydot(cg.G)
return {
"graph": cg.G,
"edges": [(str(cg.G.nodes[i][0]), str(cg.G.nodes[j][0]))
for i, j in cg.G.find_edges()],
"independencies": cg.check_ci_deviations()
}
Power Analysis for Observational Studies
# Power calculation for DiD with panel data
def power_did(n_units, n_periods, effect_size, rho=0.5, sigma=1, alpha=0.05):
"""
Power for difference-in-differences.
n_units: total units (treated + control)
n_periods: pre + post periods
effect_size: minimum detectable effect
rho: within-unit correlation over time
sigma: outcome standard deviation
"""
# Effective sample size accounting for clustering
deff = 1 + (n_periods - 1) * rho # Design effect
n_eff = n_units * n_periods / deff
se = sigma * np.sqrt(1/n_eff + 1/n_eff)
t_crit = stats.t.ppf(1 - alpha/2, df=n_eff - 2)
power = 1 - stats.nct.cdf(t_crit, df=n_eff - 2, nc=effect_size/se)
return power
# Power for RDD
def power_rdd(n, effect_size, bandwidth_prop=0.5, alpha=0.05):
"""
Power for regression discontinuity.
n: total sample size
effect_size: jump at cutoff (in outcome SD units)
bandwidth_prop: proportion of data near cutoff used
"""
n_eff = n * bandwidth_prop * 0.5 # ~50% on each side of cutoff
se = 1.08 * np.sqrt(1/n_eff) # RDD SE approximation (local linear)
t_crit = stats.t.ppf(1 - alpha/2, df=n_eff - 2)
power = 1 - stats.nct.cdf(t_crit, df=n_eff - 2, nc=effect_size/se)
return power
Decision Trees
Causal Method Selection
Data and question type?
├── RCT available → Randomized experiment (ATE/CATE)
│ ├── Need real-time optimization → Multi-armed bandit
│ └── Standard A/B → Pre-registered experiment
├── Panel data, pre/post periods + control group → DiD
│ ├── Multiple treated units + staggered adoption → Event study / staggered DiD
│ └── Single treated unit + synthetic control → Synthetic control method
├── Clear cutoff in running variable → RDD
│ └── Multiple cutoffs → Multi-cutoff RDD or RDD with covariates
├── Valid instrument available → IV / 2SLS
│ └── Multiple instruments → Over-identification tests + LIML
├── Observational with all confounders measured → PSM / IPW / Double ML
│ ├── High-dimensional confounders → Double/Debiased ML
│ └── Low-dimensional, simple matching → Propensity score matching
└── Need heterogeneous treatment effects → CATE estimation
├── Binary treatment → Causal forest, BART, meta-learners
└── Continuous treatment → Generalized random forest, kernel methods
Sensitivity Analysis Selection
What type of violation is most plausible?
├── Unobserved confounder (general)
│ └── E-value: how strong must confounder be?
├── Violation of parallel trends (DiD)
│ └── Placebo test: effect in pre-treatment period? Different control group?
├── Manipulation of running variable (RDD)
│ └── McCrary density test: discontinuity in running variable density?
├── Weak instrument (IV)
│ └── F-statistic > 10? Anderson-Rubin confidence intervals?
├── Non-random attrition
│ └── Bounds (Manski bounds, Lee bounds)
└── Multiple violations
└── Multiple robustness checks, each addressing one violation
Rules
- Always draw and justify the causal DAG before estimation
- State untestable assumptions explicitly (ignorability, exclusion, monotonicity)
- Prefer doubly robust methods when possible
- Report standard errors from bootstrap or influence functions
- Sensitivity analysis is mandatory for observational studies
- Never interpret regression coefficients causally without identification strategy
- Use domain expertise for DAG construction, not data-driven alone
- Balance check for propensity score methods (standardized mean differences)
- Placebo tests (lead outcomes, untreated units) for DiD validity
- Multiple robustness checks with different estimators
- Match method to data structure and assumptions — not all methods fit all problems
- Compute E-values for sensitivity to unobserved confounding
- Check for collider bias before adjusting for covariates
- Use causal discovery for hypothesis generation only, not confirmation
- Power analysis for observational studies is more complex than RCT power — account for clustering and design effect
References
- references/causal-frameworks.md — Causal Inference Frameworks Reference
- references/causal-inference-advanced.md — Causal Inference Advanced Topics
- references/causal-inference-fundamentals.md — Causal Inference Fundamentals
- references/causal-inference-methods.md — Causal Inference Methods Reference
- references/causal-ml.md — Causal Machine Learning Reference
- references/quasi-experimental.md — Quasi-Experimental Methods Reference
Handoff
data-science-statistical-analysis for foundational statistical methods
data-science-experimentation for RCT design and A/B testing
data-science-analytics-engineering for causal pipeline data infrastructure