This question involves analyzing CEO salary data from the wooldridge library in R, focusing on the variable ros (return on firm stock from 1988-1990). Let's break down the tasks:

1. Data Manipulation:

   • You create two new series:
     • rosneg is a binary variable where rosneg = 1 if ros <= 0 (indicating non-positive stock returns) and rosneg = 0 otherwise.
     • rosfiltered holds values of ros only when ros > 0, setting it to 0 otherwise.
   • This transformation is helpful for exploring the effect of different stock return categories on lsalary.

2. Regression Analysis:

   • Three regression models are specified:
     • Model A: $lsalary = \beta_0 + \beta_1 lsales + \beta_2 roe + \beta_3 ros + \epsilon$
     • Model B: $lsalary = \beta_0 + \beta_1 lsales + \beta_2 roe + \beta_3 rosneg + \epsilon$
     • Model C: $lsalary = \beta_0 + \beta_1 lsales + \beta_2 roe + \beta_3 ros + \beta_4 rosfiltered + \epsilon$

   Each model explores how ros (or variations of it) influences the log salary (lsalary), with other variables (lsales and roe) as controls.

3. Heteroskedasticity-Robust Standard Errors:

   • In part (b), the vcovHC() function with type = "HC0" is used for obtaining heteroskedasticity-robust standard errors, which account for any heteroskedasticity in the data, providing more reliable inference.

4. RESET Tests for Functional Form:

   • Part (c) involves performing heteroskedasticity-robust RESET tests (using squared and cubed fitted values) on each model to check for functional form misspecification. A significant RESET test result indicates a potential need for model modification.

Solution Steps:

1. Part (a): Explain how each model uses ros.

   • Model A: Directly includes ros to assess its overall effect on lsalary.
   • Model B: Uses rosneg to differentiate CEOs with non-positive returns, testing if such cases significantly impact salaries.
   • Model C: Includes both ros and rosfiltered, allowing separation of the effects of positive vs. non-positive returns.

2. Part (b): Run each regression and interpret the coefficients of ros, rosneg, or rosfiltered, particularly focusing on how ros influences lsalary.

3. Part (c): Apply RESET tests to validate model specification, ensuring that lsalary is appropriately predicted by the chosen model form.

If you need code examples or help setting up these regressions in R, let me know!

Related Questions

1. What is the purpose of using heteroskedasticity-robust standard errors in regression analysis?
2. How does the RESET test help identify model misspecification?
3. Why might we use a binary variable like rosneg instead of the original ros?
4. What are potential limitations of interpreting rosfiltered in the regression models?
5. How would you interpret the impact of lsales and roe on lsalary in these models?

Tip:

When handling multiple transformations of a variable (like ros, rosneg, and rosfiltered), keep track of their individual interpretations to make comparisons clear during analysis.