MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Earnings Equation Exploration**

Consider an earnings equation (wage, dollars per hour) consisting of a gender dummy (female = 1), years of education, and an interaction term (female*educ):

\[ wage_i = \beta_0 + \beta_1 female_i + \beta_2 educ_i + \beta_3 female_i \ast educ_i + \epsilon_i. \]

### Key Points to Explore:

1. **Predicted Wages for Males and Females:**
   - For males (\(female = 0\)), the equation simplifies to:
     \[ wage_i = \beta_0 + \beta_2 educ_i + \epsilon_i. \]
   - For females (\(female = 1\)), the equation becomes:
     \[ wage_i = \beta_0 + \beta_1 + (\beta_2 + \beta_3) educ_i + \epsilon_i. \]

2. **Gender Wage Differential:**
   - The difference in predicted wages between males and females is:
     \[ \beta_1 + \beta_3 educ_i. \]

3. **Convergence Assumptions:**
   - To analyze convergence of female earnings to male earnings, assume that after a certain level of education, the earnings differential diminishes.
   - This would imply: \(\beta_1\) is negative or small, and \(\beta_3\) is positive, indicating that education has a larger impact on female wages than male wages.

4. **Diagram Illustration:**
   - **X-axis:** Years of Education
   - **Y-axis:** Wage
   - **Two lines showing wage vs. education:**
     - **Males:** Slope \(\beta_2\)
     - **Females:** Slope \(\beta_2 + \beta_3\)
   - Initial gap at zero education determined by \(\beta_1\), with convergence as education increases if \(\beta_3 > 0\).

### Considerations

- Analyze how education affects both genders differently.
- Explore policy implications on education's role in reducing the wage gap.
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Transcribed Image Text:**Earnings Equation Exploration** Consider an earnings equation (wage, dollars per hour) consisting of a gender dummy (female = 1), years of education, and an interaction term (female*educ): \[ wage_i = \beta_0 + \beta_1 female_i + \beta_2 educ_i + \beta_3 female_i \ast educ_i + \epsilon_i. \] ### Key Points to Explore: 1. **Predicted Wages for Males and Females:** - For males (\(female = 0\)), the equation simplifies to: \[ wage_i = \beta_0 + \beta_2 educ_i + \epsilon_i. \] - For females (\(female = 1\)), the equation becomes: \[ wage_i = \beta_0 + \beta_1 + (\beta_2 + \beta_3) educ_i + \epsilon_i. \] 2. **Gender Wage Differential:** - The difference in predicted wages between males and females is: \[ \beta_1 + \beta_3 educ_i. \] 3. **Convergence Assumptions:** - To analyze convergence of female earnings to male earnings, assume that after a certain level of education, the earnings differential diminishes. - This would imply: \(\beta_1\) is negative or small, and \(\beta_3\) is positive, indicating that education has a larger impact on female wages than male wages. 4. **Diagram Illustration:** - **X-axis:** Years of Education - **Y-axis:** Wage - **Two lines showing wage vs. education:** - **Males:** Slope \(\beta_2\) - **Females:** Slope \(\beta_2 + \beta_3\) - Initial gap at zero education determined by \(\beta_1\), with convergence as education increases if \(\beta_3 > 0\). ### Considerations - Analyze how education affects both genders differently. - Explore policy implications on education's role in reducing the wage gap.
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