Final Exam ECO321 Spring 2016 – The following estimated equation was obtained by OLS regression

Final Exam ECO321 Spring 20161. The following estimated equation was obtained by OLS regression using quarterly data for 1958to 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 ofsquares 40.a. Test the hypothesis that the coefficient on X2t equals −4.b. when three seasonal dummy variables are added and the equation reestimated, the explainedsum of squares rose to 90. Define the seasonal dummy variables and write down the regressionequation (using β’s for coefficients). Test the null hypothesis of no seasonality.2. State the Gauss-Markov Assumptions A1-A4 for SLRM, and provide discussion of the meaning andimportance of each one.3. What is the different between interpretation of coefficient in SLRM and MLRM? How does itrelate to omitted variable bias? How about a linear versus nonlinear multiple regression modelcoefficients? (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-linearB) 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 yearsofeducation of the mother and father respectively and familyincome is the income of thefamily.We expect β1 < 0, β2 < 0 and β3 < 0.a. What is the effect of omitting familyincome from the regression model on β1 andβ2 if eachparent’s education is positively correlated with family income?b. Write the null hypothesis, restricted regression, test statistic and degrees of freedom for a testof the hypothesis that the effect of mother’s education equals the effect of father’seducation.6. The Stata file ceosalary.dta contains data on the characteristics of 177 chief executive officers,which we will use to examine the effects of firm performance on CEO salary. The variables in thedataset include 1. salary (1990 compensation, $1000s), 2. age (in years), 3. college (=1 if attendedcollege), 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 effects of sales and market value on salaries of CEOsFinal Exam ECO321 Spring 2016b. Add prof its and ceoten to the model. Which firm characteristics are significant determinantof salaries? Interpret the effect 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 effects of ceoten and comtend. Using an appropriate restricted regression, test the hypothesis that none of the 3 firmperformance variables matter for CEO salaries.e. Using an appropriate restricted regression, test the hypothesis that comten and ceoten have equaland opposite effects on log(salary).