Introductory Applied Econometrics EEP/IAS 118 Spring 2014

Andrew Crane-Droesch, Section #5, Feb 26, 2014

Omitted Variable Bias (OVB)

Part I: Understanding OVB

• Key Assumption: E[u|x] = 0 for unbiased estimates.
• Problem: If a key variable is omitted, E[β1] ≠ β1 (biased estimate).
• Solution: Include the omitted variable in the model to remove bias.

Part II: OVB and the SLR Assumptions

• Focus on SLR1-5 assumptions.
• SLR4 Failure: Omitting variables leads to E[u|X] ≠ 0.
• Population Model: y = β0 + β1x + u.
• Sample Regression: yi = β0 + β1xi.
• Formula for β1: Demonstrated using covariance and variance.
• Expectation of β1: On average, estimates equal true parameter if SLR.1-4 hold.

Reality Check: When SLR.4 Fails

• Expectation with Omission: Adds extra terms, causing bias.
• E[β1] = β1 + β2E[Σ(xi-x)zi/Σ(xi-x)xi]
• The omitted variable z affects the outcome y.

Example: OVB in Wage Analysis

• Data: Wage data from WAGE1.dta, focus on gender and omitted variable tenure.
• Correlation: Examined between wages, gender, and tenure.
• Regression Examples: Run with and without tenure to show bias.
• Bias Check: Calculated using regression outputs.

Intuition for OVB

• Analogy: Archer aiming off target due to omitted variables.
• Simulation: Repeated estimation with different samples to show biased and unbiased distributions.

Take Home Practice

• Exercise: Impact of seatbelt laws on traffic fatalities.
• Factors: Consider other variables that could affect fatalities and how they correlate with primary laws.

Confidence Intervals

• Concept: Address randomness and variability in estimates.
• Interpretation: Confidence intervals show likely range for true parameter.
• Central Limit Theorem: Sample means form normal distribution.
• Standardization and Normal Distribution: Use for interpretation.
• Student t Distribution: Used when sample variance is estimated.
• Formula for Confidence Interval: CI W = [x - cW(s/√n), x + cW(s/√n)]

Example

• Sample Data: UCB student heights to calculate a 95% confidence interval.
• Steps: Determine confidence level, compute estimates, find c from t-table, and plug values.

Practice

• Calculate a 99% confidence interval for housing prices in the Bay Area using given data.

Appendix

• Discusses facts used in omitted variable bias calculations.