Economic Policy Impact: Minimum Wage Analysis

This case study demonstrates how CAIS analyzes the causal impact of minimum wage policies using regression discontinuity design. We’ll explore how the agent identifies and exploits policy discontinuities for causal identification.

Problem Statement

Research Question: What is the causal effect of minimum wage increases on employment levels?

Context: Different states implemented minimum wage increases at different times, creating geographic discontinuities at state borders. We can exploit these discontinuities to identify causal effects while controlling for other economic factors.

Policy Relevance: Understanding the employment effects of minimum wage policies is crucial for evidence-based policy making and has been a subject of extensive economic debate.

Dataset Overview

Source: State-level employment and wage data with geographic identifiers Sample Size: 2,847 county-month observations Treatment: Minimum wage increase (binary) Outcome: Employment rate (percentage) Key Variables:

• employment_rate: County employment rate (%)

• min_wage_increase: Binary indicator for minimum wage increase

• distance_to_border: Distance to state border (miles)

• population: County population

• median_income: Median household income

• unemployment_rate: Baseline unemployment rate

import pandas as pd
from causal_agent import CausalAgent

# Load the minimum wage dataset
df = pd.read_csv('data/all_data/min_wage_data.csv')

print("Dataset shape:", df.shape)
print("\nTreatment distribution:")
print(df['min_wage_increase'].value_counts())

print("\nRunning variable summary:")
print(df['distance_to_border'].describe())

Agent Decision-Making Process

Let’s trace through how CAIS identifies the regression discontinuity design opportunity.

Step 1: Initial Data Analysis

The agent examines the dataset structure and identifies the discontinuous treatment assignment:

agent = CausalAgent()

# Agent performs automatic data analysis
analysis_result = agent.analyze(
    data=df,
    treatment='min_wage_increase',
    outcome='employment_rate',
    verbose=True
)

Agent Output:

🔍 CAIS Data Analysis
=====================

Dataset Characteristics:
- Sample size: 2,847 observations
- Treatment variable: 'min_wage_increase' (binary)
- Outcome variable: 'employment_rate' (continuous)
- Missing values: 0.8% (manageable)

Treatment Assignment Analysis:
- Treatment group: 1,423 counties (50.0%)
- Control group: 1,424 counties (50.0%)
- Assignment appears NON-RANDOM ⚠️

🔍 Searching for Running Variables...

Potential Running Variable Detected:
- Variable: 'distance_to_border'
- Type: Continuous
- Range: [-150.2, 149.8] miles
- Cutoff candidate: 0 miles (state border)

📊 Discontinuity Analysis:
- Treatment probability jump at cutoff: 0.98
- Sharp discontinuity detected ✓
- Bandwidth assessment: Optimal = 45.2 miles

Step 2: Decision Tree Navigation

The agent navigates the decision tree and identifies the RDD opportunity:

        flowchart TD
    A[Min Wage Data] --> B{Is this randomized?}
    B -->|No ✗| C{Panel data available?}
    C -->|No ✗| D{Running variable with cutoff?}
    D -->|Yes ✓| E{Sharp discontinuity?}
    E -->|Yes ✓| F[Regression Discontinuity<br/>Design]

    style A fill:#e3f2fd
    style B fill:#ffebee
    style C fill:#ffebee
    style D fill:#fff3e0
    style E fill:#fff3e0
    style F fill:#e8f5e8
    

Decision Logic:

1. Randomization Check: ❌ FAILED - Treatment assignment based on geographic location - Systematic differences across state borders - Conclusion: This is observational data

2. Panel Data Check: ❌ NOT AVAILABLE - Cross-sectional data at single time point - Cannot use difference-in-differences - Need alternative identification strategy

3. Running Variable Check: ✅ DETECTED - Distance to state border is continuous running variable - Treatment assignment changes sharply at border (cutoff = 0) - Clear discontinuous assignment rule

4. Discontinuity Assessment: ✅ SHARP DISCONTINUITY - Treatment probability jumps from ~0.02 to ~0.98 at border - Sharp cutoff rather than fuzzy discontinuity - Suitable for RDD analysis

5. Method Selection: Regression Discontinuity Design

Agent Reasoning:

🎯 Method Selection: Regression Discontinuity Design

Why this method?
✓ Sharp discontinuity in treatment assignment at state border
✓ Running variable (distance to border) is continuous
✓ Treatment assignment rule is deterministic and known
✓ Can control for smooth functions of running variable

RDD Assumptions:
✓ Sharp cutoff: Treatment jumps discontinuously at border
✓ Continuity: Other factors smooth through the cutoff
✓ No manipulation: Counties can't manipulate distance to border
✓ Local randomization: Units near cutoff are comparable

Step 3: RDD Specification and Validation

The agent implements RDD with appropriate specification choices:

# Agent automatically implements RDD analysis
rdd_results = analysis_result.get_rdd_analysis()

print("RDD Specification:")
print(rdd_results.specification)

RDD Implementation:

📊 Regression Discontinuity Implementation
==========================================

Running Variable: distance_to_border (miles)
Cutoff: 0 miles (state border)
Treatment: min_wage_increase (binary)
Outcome: employment_rate (%)

Specification Choices:
- Bandwidth: 45.2 miles (MSE-optimal)
- Polynomial order: 1 (linear)
- Kernel: Triangular
- Sample size: 1,847 observations within bandwidth

Model Equation:
employment_rate = α + β×min_wage_increase + γ×distance_to_border +
                 δ×(distance_to_border × min_wage_increase) + ε

Continuity Checks:

🔍 RDD Assumption Validation
============================

1. Continuity of Covariates:
- Population: No jump at cutoff (p = 0.234)
- Median income: No jump at cutoff (p = 0.456)
- Baseline unemployment: No jump at cutoff (p = 0.123)
✓ Covariates continuous at cutoff

2. Density Test (McCrary):
- Test statistic: 0.089
- P-value: 0.234
✓ No evidence of manipulation

3. Bandwidth Sensitivity:
- 30 miles: -1.23 [-2.45, -0.01]
- 45 miles: -1.34 [-2.12, -0.56] (selected)
- 60 miles: -1.28 [-1.98, -0.58]
✓ Results stable across bandwidths

Step 4: Treatment Effect Estimation

With validated RDD design, the agent estimates the causal effect:

# Get RDD treatment effect results
results = analysis_result.get_results()

print("RDD Results:")
print(results.summary())

Causal Effect Results:

🎯 RDD Treatment Effect Results
===============================

Local Average Treatment Effect (LATE): -1.34 percentage points
95% Confidence Interval: [-2.12, -0.56]
P-value: 0.001

Interpretation:
Minimum wage increases cause a 1.34 percentage point
reduction in employment rates at the state border.
This represents a statistically significant negative
employment effect of minimum wage policy.

Effect Size:
- Relative to baseline: -2.1% employment reduction
- Economic significance: Moderate negative effect
- Policy implication: Employment-wage tradeoff exists

Visual Evidence:

📈 RDD Plot Interpretation
==========================

Key Visual Features:
✓ Clear discontinuous jump in employment at border
✓ Smooth trends on both sides of cutoff
✓ No obvious confounding jumps in covariates
✓ Adequate density of observations near cutoff

Treatment Effect Visualization:
- Left of cutoff (no min wage): ~63.2% employment
- Right of cutoff (min wage): ~61.9% employment
- Discontinuous jump: -1.34 percentage points

Method Exclusion Examples

Let’s examine why other methods were excluded for this dataset:

Difference-in-Differences

Why Excluded:

❌ Difference-in-Differences: EXCLUDED

Reason: Insufficient temporal variation
- Requires: Panel data with pre/post treatment periods
- Available: Cross-sectional data at single time point
- Missing: Time series variation in treatment
- Alternative: Could work with panel data over time

What Would Be Needed: - Multiple time periods before and after policy implementation - Variation in timing of minimum wage increases across states - Parallel trends assumption between treatment and control states

Instrumental Variables

Why Excluded:

❌ Instrumental Variables: EXCLUDED

Reason: RDD provides cleaner identification
- Geographic discontinuity is stronger than potential instruments
- No need for additional instruments when RDD is available
- RDD assumptions more credible than IV exclusion restriction
- Conclusion: RDD is preferred identification strategy

When IV Might Be Preferred: - If geographic discontinuity were fuzzy rather than sharp - If other factors also jumped discontinuously at border - If manipulation of running variable were suspected

Propensity Score Methods

Why Excluded:

❌ Propensity Score Methods: EXCLUDED

Reason: Geographic treatment assignment
- Treatment determined by location, not individual characteristics
- Propensity scores would be deterministic (0 or 1)
- No meaningful variation to model treatment probability
- RDD exploits geographic variation more appropriately

When Matching Might Work: - If analyzing individual-level data within states - If treatment varied by individual characteristics - If geographic variation were not available

Robustness Analysis

The agent performs comprehensive RDD robustness checks:

Bandwidth Sensitivity

# Agent tests multiple bandwidths
robustness = analysis_result.get_robustness_checks()

print("Bandwidth Sensitivity:")
for check in robustness['bandwidth_tests']:
    print(f"Bandwidth {check.bandwidth}: {check.estimate} {check.ci}")

Bandwidth Results:

🔍 Bandwidth Sensitivity Analysis
=================================

Bandwidth Selection Methods:
- MSE-optimal: 45.2 miles → -1.34 [-2.12, -0.56]
- CER-optimal: 38.7 miles → -1.41 [-2.28, -0.54]
- Rule-of-thumb: 52.1 miles → -1.28 [-1.95, -0.61]

Manual Bandwidth Tests:
- 30 miles: -1.23 [-2.45, -0.01] (wider CI, smaller sample)
- 60 miles: -1.28 [-1.98, -0.58] (similar estimate)
- 75 miles: -1.19 [-1.87, -0.51] (similar estimate)

Conclusion: Results robust across reasonable bandwidths

Polynomial Order Sensitivity

📊 Polynomial Order Robustness
==============================

Specification Tests:
- Linear (order 1): -1.34 [-2.12, -0.56] (selected)
- Quadratic (order 2): -1.28 [-2.18, -0.38] (similar)
- Cubic (order 3): -1.41 [-2.35, -0.47] (similar)

Model Selection:
- AIC favors: Linear specification
- BIC favors: Linear specification
- Cross-validation: Linear performs best

Conclusion: Linear specification appropriate

Placebo Tests

🧪 Placebo and Falsification Tests
==================================

Placebo Cutoffs:
- -25 miles: 0.12 [-0.89, 1.13] (not significant)
- +25 miles: -0.23 [-1.34, 0.88] (not significant)
- -50 miles: 0.34 [-0.78, 1.46] (not significant)

Placebo Outcomes:
- Population density: 0.05 [-0.12, 0.22] (not significant)
- Median income: 234 [-1,234, 1,702] (not significant)
- Education levels: 0.02 [-0.15, 0.19] (not significant)

Conclusion: No spurious discontinuities detected

Decision Tree Alternative Scenarios

Let’s explore how different data characteristics would change the analysis:

Scenario 1: Fuzzy Discontinuity

Hypothetical: Treatment probability jumps but doesn’t reach 100%

        flowchart TD
    A[Fuzzy RDD Data] --> B{Is this randomized?}
    B -->|No ✗| C{Panel data available?}
    C -->|No ✗| D{Running variable with cutoff?}
    D -->|Yes ✓| E{Sharp discontinuity?}
    E -->|No ✗| F{Fuzzy discontinuity?}
    F -->|Yes ✓| G[Fuzzy Regression<br/>Discontinuity]

    style A fill:#e3f2fd
    style B fill:#ffebee
    style C fill:#ffebee
    style D fill:#fff3e0
    style E fill:#ffebee
    style F fill:#fff3e0
    style G fill:#e8f5e8
    

Alternative Analysis: - Method: Fuzzy RDD (instrumental variables approach) - First stage: Running variable predicts treatment probability - Second stage: Predicted treatment affects outcome - Interpretation: Local average treatment effect for compliers

Scenario 2: Panel Data Available

Hypothetical: Same counties observed before and after policy changes

        flowchart TD
    A[Panel RDD Data] --> B{Is this randomized?}
    B -->|No ✗| C{Panel data available?}
    C -->|Yes ✓| D{Treatment timing varies?}
    D -->|Yes ✓| E{Also running variable?}
    E -->|Yes ✓| F[Difference-in-Differences<br/>or RDD]

    style A fill:#e3f2fd
    style B fill:#ffebee
    style C fill:#fff3e0
    style D fill:#fff3e0
    style E fill:#fff3e0
    style F fill:#e8f5e8
    

Method Choice Considerations: - DiD: Exploits timing variation, controls for fixed effects - RDD: Exploits geographic variation, local identification - Combined: Could use both for robustness - Agent would likely prefer DiD for stronger identification

Economic Interpretation

Policy Implications

Employment Effects: - Magnitude: 1.34 percentage point reduction - Baseline employment: 63.2% - Relative effect: 2.1% reduction in employment - Economic significance: Moderate negative effect

Cost-Benefit Analysis:

💰 Economic Impact Assessment
=============================

Employment Effects:
- Jobs lost per county: ~89 jobs (based on labor force)
- Total affected workers: ~164,000 across all counties
- Unemployment increase: 1.34 percentage points

Wage Effects (for remaining workers):
- Minimum wage increase: $2.50/hour average
- Annual wage gain: ~$5,200 per worker
- Total wage gains: ~$1.2 billion

Net Welfare Effects:
- Worker benefits: Higher wages for employed
- Worker costs: Some job losses
- Employer costs: Higher labor costs
- Consumer effects: Potentially higher prices

Policy Recommendations:

1. Gradual Implementation: Phase in wage increases to minimize employment disruption

2. Targeted Support: Provide job training for displaced workers

3. Regional Variation: Consider local economic conditions

4. Monitoring: Track long-term employment and wage effects

Limitations and External Validity

RDD-Specific Limitations:

1. Local Effects: Results only apply near state borders

2. External Validity: May not generalize to interior regions

3. Short-term Effects: Cannot capture long-term adjustments

4. Spillover Effects: May miss cross-border labor mobility

Economic Considerations:

⚠️ Interpretation Caveats
=========================

Geographic Limitations:
- Results specific to border counties
- May differ from state-wide effects
- Border economies may be unique

Temporal Limitations:
- Cross-sectional snapshot
- Cannot capture dynamic adjustments
- Firms may adapt over time

Equilibrium Effects:
- Partial equilibrium analysis
- May miss general equilibrium responses
- Price and wage adjustments not captured

Comparison with Literature

Existing Research: - Card & Krueger (1994): No employment effects using DiD - Neumark & Wascher (2000): Negative employment effects - Dube et al. (2010): Mixed results depending on method

CAIS Contribution: - Systematic method selection based on data structure - Transparent identification strategy - Comprehensive robustness analysis - Replicable methodology

Learning Objectives Achieved

After working through this case study, you should understand:

✅ Regression Discontinuity: How to identify and exploit policy discontinuities

✅ Running Variables: How to detect continuous assignment variables

✅ Sharp vs. Fuzzy: Different types of discontinuous treatment assignment

✅ Bandwidth Selection: How to choose optimal bandwidth for RDD

✅ Assumption Testing: How to validate RDD assumptions

✅ Economic Interpretation: How to translate RDD results into policy insights

Next Steps

1. Explore Fuzzy RDD: Analyze cases with imperfect compliance

2. Try Alternative Bandwidths: Test sensitivity to bandwidth choice

3. Examine Heterogeneity: Look for effects across different county types

4. Read Method Documentation: Deep dive into ../methods/quasi_experimental/regression_discontinuity

Related Case Studies: - Education Policy Analysis: Learning Mindset Intervention - Randomized experiment analysis - Healthcare Treatment Effects: Hospital Treatment Analysis - Propensity score matching - Marketing Campaign Evaluation: Instrumental Variables Analysis - Instrumental variables approach

Download Materials: - Minimum Wage Dataset - Complete Analysis Notebook - Replication Code