1. The following estimated equation was obtained by OLS regression using quarterly data for 1958 to 1976 inclusive:
Yt = 2.20 + 0.104X1t - 3.48X2t + 0.34X3t.
(3.4) (0.005) (2.2) (0.15)
Standard errors are in parentheses. The explained sum of squares is 80 and the residual sum of squares 40.
a. Test the hypothesis that the coefficient on X2t equals -4.
b. When three seasonal dummy variables are added and the equation re-estimated, the explained sum of squares rose to 90. Define the seasonal dummy variables and write down the regression equation (using β's for coe?cients). Test the null hypothesis of no seasonality.
2. State the Gauss-Markov Assumptions A1-A4 for SLRM, and provide discussion of the meaning and importance of each one.
3. What is the different between interpretation of coefficient in SLRM and MLRM? How does it relate to omitted variable bias? How about a linear versus nonlinear multiple regression model coefficients? (Quadratic). What is the role of controls?
4. How do you choose between log-linear model and log-log model? How about linear log-linear? And how about linear-log and log-log? Why? How do you interpret coefficients of a A) log-linear B) log-log and C) linear-log model?
5. The following equation represents a regression model for the number of children in a family:
Children = β0 + β1motherseduc + β2fatherseduc + β3familyincome + u,
Where children is the number of children, motherseduc and fatherseduc are the years of education of the mother and father respectively and familyincome is the income of the family. We expect β1 < 0, β2 < 0 and β3 < 0.
a. What is the effect of omitting family income from the regression model on β1 and β2 if each parent's education is positively correlated with family income?
b. Write the null hypothesis, restricted regression, test statistic and degrees of freedom for a test of the hypothesis that the effect of mother's education equals the effect of father's education.
6. The Stata file ceosalary.dta contains data on the characteristics of 177 chief executive o?cers, which we will use to examine the e?ects of firm performance on CEO salary. The variables in the dataset include 1. salary (1990 compensation, $1000s), 2. age (in years), 3. college (=1 if attended college), 4. grad (=1 if attended graduate school), 5. comten (years with company), 6. ceoten (years as ceo with company), 7. sales (1990 firm sales, millions), 8. prof its (1990 profits, millions), 9. mktval (market value, end 1990, millions).
a. Estimate a regression of salary on firm sales and market value in constant elasticity (log-log) form. Interpret the e?ects of sales and market value on salaries of CEOs
b. Add prof its and ceoten to the model. Which firm characteristics are significant determinant of salaries? Interpret the e?ect of an additional year of CEO tenure on salaries.
c. Estimate a regression of log(salary) on log(sales), log(mktval), prof mar (prof its/sales), comten and ceoten. Interpret the e?ects of ceoten and comten
d. Using an appropriate restricted regression, test the hypothesis that none of the 3 firm performance variables matter for CEO salaries.
e. Using an appropriate restricted regression, test the hypothesis that comten and ceoten have equal and opposite e?ects on log(salary).
Attachment:- ceosalary.rar