EC3301: Class Test 2

• How can qualitative information be incorporated into regression analysis?

  By using dummy variables
• What is the dummy variable trap?

  A situation where the model cannot be estimated due to perfect collinearity
• What must be done when using dummy variables in regression analysis?

  One category must always be omitted as the base/benchmark category
• What is the base category when using dummy variables for gender?

  Men
• What does the equation male + female equal in the context of dummy variables?

  1

  
• Why should dummy variables not be logged?

  Because they only take values of 0 or 1
• What does the equation for hrsemp represent in the context of training grants?

  It estimates hours of training based on whether a firm received a training grant
• What does the variable 'grant' equal in the context of the hrsemp equation?

  1 if the firm received a training grant, 0 if not
• What does it mean if a grant receiving firm offers 26.25 more hours of training?

  It indicates a positive effect of receiving a training grant
• What does it imply if married women earn 19.8% less than single men?

  It suggests a wage disparity based on marital status and gender
• What are the steps for using dummy variables for multiple categories in regression analysis?

  1. Define membership in each category by a dummy variable
  2. Leave out one category to become the base category
• What do interaction terms allow in regression analysis?

  They allow for different slopes for different groups
• What does the interaction term in wage equations indicate?

  It indicates the return to education is the same for men and women

  
• What does interacting both the intercept and slope with the female dummy enable?

  It enables modeling completely independent wage equations for men and women

  
• What does the estimated wage equation with interaction term suggest about education and gender?

  There is no evidence against the hypothesis that the return to education is the same for men and women

  
• What must be done to assess the significance of lower pay for women at different education levels?

  The interaction term must be recentered around the average education level
• What is the null hypothesis in testing for differences in regression functions across groups?

  All interaction effects are zero, meaning the same regression coefficients apply to both groups
• What is the Chow-Test used for?

  To test if the regression functions are the same across groups
• What does the Chow-Test assume about error variance?

  It assumes a constant error variance across groups
• What happens to OLS under heteroskedasticity?

  OLS remains unbiased and consistent
• How does heteroskedasticity affect the interpretation of R²?

  Interpretation of R² remains unchanged
• What is the consequence of heteroskedasticity on F-tests and t-tests?

  They are no longer valid
• What is the main topic of Lecture 8 (week 8)?

  Functional form misspecification and outliers
• What is the implication of standard errors under heteroskedasticity?

  Standard errors reported by OLS may not be valid for constructing t-tests and confidence intervals
• What is the purpose of heteroskedasticity-robust inference after OLS?

  To provide standard errors and statistics that are robust to heteroskedasticity
• What are the main readings for this lecture?

  Sections 9.1 and 9.5c
• When are the office hours for contact?

  Wednesday 11.00-12.00 and Thursday 3.00-4.00
• What is conditional error variance unaffected by?

  Heteroscedasticity
• What is functional form misspecification in regression analysis?

  • Occurs when the relationship between dependent and explanatory variables has the wrong functional form.
  • Correct variables are used, but the functional form is incorrect.
  • Can lead to biased estimators.
• What does heteroscedasticity refer to in the context of regression analysis?

  It refers to the conditional error variance.
• What happens if the correct specification includes quadratics or logs?

  It leads to biased estimators if not included in the model.
• What are the consequences of heteroscedasticity on OLS?

  OLS remains unbiased and consistent.
• If the initial model is $y =$$\beta_0 +$$\beta_1 x_1 +$$\beta_2 x_2 +$$u$, what might be added to improve it?


  Quadratic and interaction terms
• How are the interpretations of $R^2$ and $\bar{R}^2$ affected by heteroscedasticity?


  The interpretations remain unchanged.
• Why do $R^2$ and $\bar{R}^2$ remain unchanged under heteroscedasticity?


  Because they estimate the population $R^2$ based on unconditional variances.
• Why can't all non-linearities be captured by adding quadratic and interaction terms?

  Because it uses up degrees of freedom and may not work if the dependent variable is modified.
• What is the RESET test used for?

  To test for functional form misspecification
• What does it mean that OLS is no longer BLUE under heteroscedasticity?

  It means OLS is not the Best Linear Unbiased Estimator.
• How does the RESET test work?

  It includes squares and possibly higher order fitted values in the regression.
• What happens to F-tests, t-tests, and confidence intervals under heteroscedasticity?

  They are no longer valid.