Teaching Notes for Applied Econometrics and Economic Modelling Lab Session - Day 4

Session 1: Discovering the Wage Gap Problem (45 min)

1. Warm-up: Regression Verification (10 min)

• Activity:

  • Advertising-Sales Data set

  • Olympic Times Data set

  • Wage Data set

  • Use GRETL to verify two pre-calculated regressions:

    1. Advertising → Sales
       
    2. Year → Olympic Times
       
• Key Question:
  “What important variables might be missing from these simple models?”

2. Wage Data Exploration (35 min)

A. Initial Data Inspection
- Compare distributions:
- Raw wage (right-skewed) vs. log(wage) (normalized)
- Why log? “Economic effects are multiplicative”

B. Visualizing the Gap
- Create side-by-side boxplots (Male vs. Female wages)
- Guide students to observe:
- Median difference
- Spread/variability
- Outliers

C. First Regression
- Run: log(wage) = 4.73 - 0.25Female
- Calculate: e^(-0.25) ≈ 0.78 → 22% wage gap
- Critical Discussion:
“Is this entire gap due to discrimination? What might be missing?”

D. Identifying Key Confounders
1. Education Levels
- Cross-tabulation shows:
- 48% women vs. 34% men in lowest education tier
- “Higher education → higher wages”

2. Part-Time Work
   • 45% women vs. 20% men work part-time
     
   • “Part-time status → lower wages”

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Session 2: Diagnosing the Problem (45 min)

3. Core Conceptual Framework (20 min)

A. Total vs. Partial Effects
- Total Effect (Simple Regression):
- “What’s the overall gap society observes?”
- Policy use: Assessing broad inequality

• Partial Effect (Multiple Regression):
  • “Is there discrimination after accounting for qualifications?”
    
  • Legal use: Proving workplace bias

B. Omitted Variable Bias
1. Visualization:
Gender → Wage ↘ ↙ Education Part-Time

2. Bias Directions:
   • Education Bias: Women ↓ education → wages ↓ → exaggerates gap
     
   • Part-Time Bias: Women ↑ part-time → wages ↓ → exaggerates gap

4. Hands-on Residual Analysis (20 min)

GRETL Steps:
1. Save residuals from initial wage regression
2. Check:
- Residuals vs. Education (expect positive correlation)
- Residuals vs. Part-Time (expect negative correlation)

Teaching Insight:
“If residuals correlate with other variables, our model is incomplete!”

5. Wrap-up & Preview (5 min)

• Summary Table:

Concept	Simple Regression	Multiple Regression
What It Measures	Total wage gap	Direct gender effect
Key Limitation	Omitted variables	Needs more data

• Next Session Preview:
  “Now that we see the problem, how do we fix it? Next time: Multiple regression in GRETL!”