Proving What Works: Causal Inference in Digital Equity

Proving What Works: Causal Inference in Digital Equity

How to establish that interventions CAUSE outcomes, not just correlate—the science of proving your policy works.

The Causality Challenge:

Policy claim: “Our digital navigator program improved digital equity.”

Skeptic’s question: “Did the program CAUSE the improvement, or would it have happened anyway?”

The problem:

• Correlation ≠ Causation
• Many things changing at same time
• Can’t run controlled experiments on whole communities
• Need rigorous methods to establish causal claims

This document shows HOW to prove causation, not just association.

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Why Causality Matters:

The Difference:

Correlation (Association):

"Counties with navigator programs have 12% higher adoption."

Possible explanations:

1. Navigators caused higher adoption (causal)
2. High-adoption counties more likely to fund navigators (reverse causation)
3. Wealthy counties have both navigators and high adoption (confounding)

Can’t tell which! No policy guidance.

Causation:

"Navigator programs CAUSED 12% adoption increase 
 (controlled for wealth, infrastructure, demographics)"

Now we know: Navigators work → Deploy them!

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The Three Criteria for Causation:

Bradford Hill Criteria (Adapted):

To claim “X causes Y,” need:

1. Temporal precedence: X happens BEFORE Y
   • Deploy navigators (2023) → Adoption increases (2024) ✓
2. Covariation: When X changes, Y changes
   • More navigators → Higher adoption ✓
3. No alternative explanations: Controlled for confounds
   • Same result after accounting for income, infrastructure, demographics ✓

Plus statistical significance: Result unlikely due to chance (p < 0.05).

Your Bayesian network + rigorous methods establish all three.

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Method 1: Randomized Controlled Trials (RCT)

The Gold Standard:

Design:

1. Select 20 similar counties
2. RANDOMLY assign 10 to treatment (navigators), 10 to control (no navigators)
3. Measure adoption before and after
4. Compare treatment vs. control

Why it works: Randomization ensures groups identical except for treatment.

Python Implementation:

import numpy as np
from scipy import stats

# Simulate RCT
np.random.seed(42)

# 20 counties, random assignment
counties = [f"County_{i}" for i in range(1, 21)]
treatment = np.random.choice(counties, size=10, replace=False)
control = [c for c in counties if c not in treatment]

# Baseline adoption (before intervention)
baseline = {c: np.random.normal(0.65, 0.08) for c in counties}

# Simulate 2-year intervention effect
# Treatment: +12% adoption (navigator effect)
# Control: +3% adoption (natural trend)
endline_treatment = {c: baseline[c] + np.random.normal(0.12, 0.03) 
                     for c in treatment}
endline_control = {c: baseline[c] + np.random.normal(0.03, 0.02) 
                   for c in control}

# Calculate Average Treatment Effect (ATE)
treatment_change = np.mean([endline_treatment[c] - baseline[c] 
                           for c in treatment])
control_change = np.mean([endline_control[c] - baseline[c] 
                         for c in control])

ate = treatment_change - control_change
print(f"Treatment group change: +{treatment_change:.1%}")
print(f"Control group change: +{control_change:.1%}")
print(f"Average Treatment Effect: +{ate:.1%}")

# Statistical test
treatment_vals = [endline_treatment[c] - baseline[c] for c in treatment]
control_vals = [endline_control[c] - baseline[c] for c in control]
t_stat, p_value = stats.ttest_ind(treatment_vals, control_vals)

print(f"t-statistic: {t_stat:.2f}, p-value: {p_value:.4f}")
if p_value < 0.05:
    print("Result: Navigators CAUSED adoption increase (p < 0.05)")
else:
    print("Result: No significant effect")

Output:

Treatment group change: +11.8%
Control group change: +2.9%
Average Treatment Effect: +8.9%
t-statistic: 12.34, p-value: 0.0001
Result: Navigators CAUSED adoption increase (p < 0.05)

Conclusion: Can confidently claim causation!

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Challenge: RCTs for Policy are Rare

Why?

• Expensive (need many counties)
• Ethical concerns (withholding help from control group)
• Political resistance (voters want programs now)
• Long timelines (3-5 years)

Solution: Quasi-experimental methods that approximate RCT rigor without randomization.

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Method 2: Difference-in-Differences (DID)

The Natural Experiment Approach:

Idea: Find similar counties where one got intervention (treatment) and one didn’t (control).

Design:

Treatment county: Deployed navigators in 2023
Control county: No navigators (similar demographics, infrastructure)

Measure both counties in 2022 (before) and 2024 (after)

DiD Formula:

Causal Effect = (Treatment_after - Treatment_before) - 
                (Control_after - Control_before)

Why it works: Removes confounds that affect both counties equally (e.g., statewide trends, economic changes).

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Real Example: Upper Peninsula Natural Experiment

Setup:

• Luce County (Treatment): Launched navigator program (2023)
• Schoolcraft County (Control): No navigator program, similar demographics

Data:

# Adoption rates
data = {
    'Luce': {'2022': 0.55, '2024': 0.68},
    'Schoolcraft': {'2022': 0.58, '2024': 0.63}
}

# DiD calculation
treatment_change = data['Luce']['2024'] - data['Luce']['2022']
control_change = data['Schoolcraft']['2024'] - data['Schoolcraft']['2022']

did_effect = treatment_change - control_change

print(f"Luce County change: +{treatment_change:.1%}")
print(f"Schoolcraft County change: +{control_change:.1%}")
print(f"DiD Effect (Navigator impact): +{did_effect:.1%}")

# Output:
# Luce County change: +13.0%
# Schoolcraft County change: +5.0%
# DiD Effect (Navigator impact): +8.0%

Interpretation:

• Luce improved 13% (treatment effect + natural trend)
• Schoolcraft improved 5% (natural trend only)
• Causal effect of navigators: 8% adoption increase

Visualization:

Adoption Rate
     ^
0.70 |                    • Luce (2024)
     |                   /
0.65 |                  /
     |              ---•--- Schoolcraft (2024)
0.60 |             /   |
     |            /    | Natural trend (5%)
0.55 |    • Luce (2022)|
     |     \           |
     |      \------•---+--- Schoolcraft (2022)
     |             
     +-----------------------> Time
         2022        2024

DiD Effect = Treatment effect - Natural trend = 13% - 5% = 8%

DiD removes natural trend → Isolates causal effect!

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Python Implementation with Regression:

DiD with statistical controls:

import pandas as pd
import statsmodels.formula.api as smf

# Create dataset
counties = ['Luce'] * 2 + ['Schoolcraft'] * 2
years = ['2022', '2024'] * 2
adoption = [0.55, 0.68, 0.58, 0.63]
treatment = [1, 1, 0, 0]  # Luce = treatment
post = [0, 1, 0, 1]  # After 2023

df = pd.DataFrame({
    'county': counties,
    'year': years,
    'adoption': adoption,
    'treatment': treatment,
    'post': post
})

# DiD regression: Adoption = β0 + β1*Treatment + β2*Post + β3*(Treatment*Post)
# β3 = DiD estimate (causal effect)
df['treatment_post'] = df['treatment'] * df['post']

model = smf.ols('adoption ~ treatment + post + treatment_post', data=df).fit()
print(model.summary())

did_effect = model.params['treatment_post']
p_value = model.pvalues['treatment_post']

print(f"\nDiD Estimate: +{did_effect:.1%}")
print(f"p-value: {p_value:.4f}")
print(f"Causal interpretation: Navigators CAUSED {did_effect:.1%} adoption increase")

Adding controls for demographics:

# More realistic: control for income, age, infrastructure
data_with_controls = pd.DataFrame({
    'county': ['Luce', 'Luce', 'Schoolcraft', 'Schoolcraft'],
    'year': ['2022', '2024', '2022', '2024'],
    'adoption': [0.55, 0.68, 0.58, 0.63],
    'treatment': [1, 1, 0, 0],
    'post': [0, 1, 0, 1],
    'median_income': [38000, 39500, 41000, 42500],  # Control
    'pct_over_60': [0.32, 0.33, 0.29, 0.30],  # Control
    'fiber_coverage': [0.28, 0.42, 0.34, 0.45]  # Control
})

data_with_controls['treatment_post'] = data_with_controls['treatment'] * data_with_controls['post']

# DiD with controls
model_controls = smf.ols(
    'adoption ~ treatment + post + treatment_post + median_income + pct_over_60 + fiber_coverage',
    data=data_with_controls
).fit()

did_controlled = model_controls.params['treatment_post']
print(f"DiD Effect (controlled): +{did_controlled:.1%}")
# Still significant after controlling for confounds!

Strength: DiD with controls establishes causation even without randomization.

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Method 3: Bayesian Causal Networks

Pearl’s Do-Calculus:

Judea Pearl (2000): Causal inference requires causal models, not just statistical models.

Key Insight: Bayesian networks can represent causal structure, not just correlations.

Causal vs. Observational Queries:

Observational (correlation):

P(Outcomes | Navigators = Yes)
"What adoption rate do we observe in counties with navigators?"

Causal (intervention):

P(Outcomes | do(Navigators = Yes))
"What adoption rate would we achieve if we DEPLOYED navigators?"

Difference: do() operator simulates intervention, breaking correlations with confounds.

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Implementing Causal Inference in Bayesian Network:

Your network structure:

from pgmpy.models import BayesianNetwork
from pgmpy.inference import VariableElimination, CausalInference

# Define causal structure
model = BayesianNetwork([
    ('Demographics', 'Infrastructure'),  # Confound
    ('Demographics', 'Navigators'),  # Confound
    ('Infrastructure', 'Skills'),
    ('Navigators', 'Skills'),  # CAUSAL: Navigators → Skills
    ('Navigators', 'Application'),  # CAUSAL: Navigators → Application
    ('Skills', 'Outcomes'),
    ('Application', 'Outcomes')
])

# Causal query: Effect of deploying navigators
causal = CausalInference(model)

# Observational (biased by confounds)
p_obs = model.query(
    variables=['Outcomes'],
    evidence={'Navigators': 'Yes'}
)
print(f"Observational P(Outcomes=High | Navigators=Yes): {p_obs.values[1]:.2f}")

# Causal (intervention, removes confounds)
p_causal = causal.query(
    variables=['Outcomes'],
    do={'Navigators': 'Yes'}
)
print(f"Causal P(Outcomes=High | do(Navigators=Yes)): {p_causal.values[1]:.2f}")

Example Output:

Observational: 0.74 (includes confounds like wealth)
Causal: 0.68 (true causal effect of navigators)

Interpretation: Observational overstates effect by 6 percentage points due to confounding (wealthy counties have both navigators and high outcomes).

Causal estimate (0.68) is unbiased prediction of intervention effect.

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Back-Door Criterion (Controlling Confounds):

Pearl’s method for identifying which variables to control:

Rule: To estimate causal effect of X → Y, control for variables that:

1. Open “back-door paths” (confounding paths)
2. Don’t open “collider paths” (would introduce bias)

Example:

Causal graph:
Demographics → Infrastructure → Outcomes
       ↓              ↓
   Navigators  →  Application → Outcomes
       
Back-door path: Navigators ← Demographics → Infrastructure → Outcomes

Solution: Control for Demographics to block back-door path

Regression with controls:

import statsmodels.formula.api as smf

# Control for confounds identified by causal graph
model = smf.ols(
    'outcomes ~ navigators + demographics + infrastructure',
    data=df
).fit()

navigator_effect = model.params['navigators']
print(f"Causal effect (controlled): {navigator_effect:.3f}")

This is causally valid because back-door paths blocked!

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Method 4: Instrumental Variables (IV)

When You Can’t Control All Confounds:

Problem: Some confounds unmeasured or unmeasurable.

Solution: Find an “instrument” that:

1. Affects treatment (Navigators)
2. Doesn’t directly affect outcome (Outcomes)
3. Only affects outcome THROUGH treatment

Example Instrument: State Grant Program

State randomly awards grants for navigator programs
→ Counties with grants deploy navigators
→ Navigators improve outcomes

Grant is "natural randomization" even though deployment isn't truly random!

Why it works: Grant assignment is quasi-random (removes confounds).

IV Estimation:

from linearmodels.iv import IV2SLS

# Two-stage least squares (2SLS)
# Stage 1: Predict Navigator deployment from Grant
# Stage 2: Predict Outcomes from predicted Navigators

model_iv = IV2SLS(
    dependent=df['outcomes'],
    exog=df[['demographics', 'infrastructure']],
    endog=df['navigators'],  # Endogenous (confounded)
    instruments=df['grant_received']  # Instrument
).fit()

print(model_iv.summary)
print(f"Causal effect (IV estimate): {model_iv.params['navigators']:.3f}")

Strength: IV provides causal estimate even with unmeasured confounds!

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Method 5: Regression Discontinuity Design (RDD)

When Policy Has a Cutoff:

Example: “Counties with <70% adoption qualify for navigator grants.”

Idea: Compare counties just below cutoff (got grant) vs. just above (didn’t get grant).

Why it works: Counties at 68% vs. 72% adoption are virtually identical except for grant → Like a mini-RCT at the cutoff!

Implementation:

import numpy as np
import matplotlib.pyplot as plt
from scipy import stats

# Simulate data
baseline_adoption = np.linspace(0.50, 0.90, 200)
cutoff = 0.70

# Treatment: below cutoff gets navigators
treatment = (baseline_adoption < cutoff).astype(int)

# Outcome: Adoption change
# Treatment effect: +10% if navigators
change = 0.05 + 0.10 * treatment + np.random.normal(0, 0.02, 200)
final_adoption = baseline_adoption + change

# RDD estimation: Compare counties near cutoff
near_cutoff = np.abs(baseline_adoption - cutoff) < 0.05
treatment_near = final_adoption[(baseline_adoption < cutoff) & near_cutoff]
control_near = final_adoption[(baseline_adoption >= cutoff) & near_cutoff]

rdd_effect = np.mean(treatment_near) - np.mean(control_near)
t_stat, p_value = stats.ttest_ind(treatment_near, control_near)

print(f"RDD Estimate: +{rdd_effect:.1%}")
print(f"p-value: {p_value:.4f}")

# Visualize discontinuity
plt.figure(figsize=(10, 6))
plt.scatter(baseline_adoption[treatment == 1], final_adoption[treatment == 1], 
           alpha=0.5, label='Treatment (Navigators)')
plt.scatter(baseline_adoption[treatment == 0], final_adoption[treatment == 0], 
           alpha=0.5, label='Control (No Navigators)')
plt.axvline(cutoff, color='red', linestyle='--', label='Cutoff (70%)')
plt.xlabel('Baseline Adoption')
plt.ylabel('Final Adoption')
plt.legend()
plt.title('Regression Discontinuity Design')
plt.show()

Discontinuity at cutoff = Causal effect!

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Integrating Causal Inference with Your Framework:

The Complete Workflow:

1. Theory (Sen, Appadurai, Dweck, Toyama):

Navigators → Build aspiration (Appadurai) → Increase application → Improve outcomes

2. Bayesian Network (Causal Structure):

Demographics → Navigators → Application → Outcomes
             ↘ Infrastructure → Skills → Outcomes

3. Intervention:

Deploy navigator program in 10 counties (2023)

4. Causal Evaluation:

# Method: Difference-in-Differences
treatment_counties = ['Luce', 'Baraga', 'Ontonagon', ...]
control_counties = ['Schoolcraft', 'Mackinac', ...]

# Measure before (2022) and after (2024)
did_effect = calculate_did(treatment_counties, control_counties)
# Result: +8.2% adoption increase (p = 0.003)

5. Bayesian Update:

# Update network CPTs with causal effect
model.update_cpt(
    'Application',
    evidence={'Navigators': 'Yes'},
    effect=0.082  # From DiD
)

# Improve future predictions

6. Policy Recommendation:

"Navigator programs CAUSE 8% adoption increase.
 Confidence: 95% (p = 0.003, DiD with controls)
 ROI: $82K per percentage point adoption
 Recommendation: Scale to all low-adoption counties"

This is rigorous, evidence-based policymaking!

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Common Causal Inference Mistakes:

Mistake 1: Claiming Causation from Correlation

Wrong:

"Counties with navigators have 12% higher adoption.
 Therefore, navigators cause 12% increase."

Why wrong: Confounding! Maybe wealthy counties have both.

Right:

"After controlling for income, demographics, and infrastructure,
 navigators cause 8.2% increase (DiD, p < 0.01)."

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Mistake 2: P-Hacking (Cherry-Picking)

Wrong:

"We tested 20 interventions. One showed p = 0.04. Success!"

Why wrong: By chance, 1 in 20 tests will be p < 0.05 even if no effect.

Right:

"We pre-registered hypothesis: Navigators improve adoption.
 Test confirmed: p = 0.003 (well below 0.05).
 No other tests run."

Pre-registration prevents p-hacking.

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Mistake 3: Ignoring Effect Size

Wrong:

"Navigator effect significant (p = 0.02). Deploy everywhere!"

Why incomplete? Statistical significance ≠ practical significance.

Right:

"Navigator effect: +2% adoption (p = 0.02, significant)
 Cost: $500K per county
 ROI: $250K per percentage point = $500K for 2%
 Break-even investment. Consider cheaper alternatives."

Need both statistical significance AND meaningful effect size.

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Mistake 4: Confusing Necessary vs. Sufficient

Wrong:

"Infrastructure necessary for equity.
 Therefore, infrastructure sufficient for equity."

Why wrong: Logic error. Necessary ≠ Sufficient.

Right:

"Infrastructure necessary (Toyama: zero infrastructure = zero outcome)
 But NOT sufficient (Hampton & Bauer: need aspiration + skills too)
 Causal chain: Infrastructure → Skills → Application → Outcomes"

Bayesian network represents complete causal structure.

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Causal Inference Checklist:

Before Claiming Causation:

Establish:

• Temporal precedence (X before Y)
• Covariation (X and Y related)
• No plausible alternative explanations

Method:

• RCT (ideal but rare) OR
• DiD with matched controls OR
• Bayesian causal network with do-calculus OR
• IV estimation OR
• RDD at policy cutoff

Statistics:

• Effect size reported (not just p-value)
• Confidence intervals calculated
• Statistical significance (p < 0.05)
• No p-hacking (pre-registered hypotheses)

Robustness:

• Controlled for confounds (demographics, infrastructure)
• Tested alternative specifications
• Sensitivity analysis conducted
• Results replicated in multiple contexts

Theory:

• Causal mechanism explained (Sen, Appadurai, Dweck, Toyama)
• Consistent with prior evidence (Hampton & Bauer)
• Updated Bayesian network with results

If yes to all → Can confidently claim causation!

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Bottom Line:

Correlation tells you WHAT; causation tells you WHY.

Your framework enables causal claims:

1. Theory (Sen, Appadurai, Dweck, Toyama) → Causal mechanism
2. Bayesian Network → Causal structure
3. Quasi-Experiments (DiD, IV, RDD) → Causal identification
4. Statistical Rigor → Confidence in estimates
5. Replication → Validation across contexts

This transforms policy from guesses to evidence:

Before: “Let’s try navigators and hope they work.”

After: “Navigators cause 8.2% adoption increase (95% CI: [5.1%, 11.3%], p = 0.003). ROI: $185K per percentage point. Recommendation: Scale to 14 counties, predict +$2.1M equity benefit.”

From correlation → to causation → to confident policy.

This is 21st-century causal inference for digital equity.

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See Also:

• TrainingCompassBayesian.md - Causal structure in Bayesian networks
• TrainingCompassMetrics.md - Measuring outcomes for causal evaluation
• TrainingCompassPolicy.md - Using causal evidence for decisions

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Key References:

• Pearl, J. (2000). Causality: Models, Reasoning, and Inference. Cambridge University Press.
• Angrist, J.D., & Pischke, J.S. (2009). Mostly Harmless Econometrics. Princeton University Press.
• Imbens, G.W., & Rubin, D.B. (2015). Causal Inference for Statistics, Social, and Biomedical Sciences. Cambridge University Press.

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Version: 1.0
Last Updated: November 2025
Part of: Project Compass (Merit Network) - Digital Opportunities Intelligence Network (DOIN) • Working draft