SECTION A: Answer all parts of this question [Total marks: 40] A. Conjecture A: "The increase in annual salary per additional year of tenure higher for a male CEO than for a female CEO given the same Age and the same ROE". Indicate which test statistic can be used to test this conjecture, Question 1 writing clearly the null and alternative hypotheses. i) In the context of the regression model yr = 8, + 82*zt + By*at + & and with [5 marks] reference to the OLS estimate of the marginal effect of X2, on yt: A. Discuss the potential consequences of the misspecification problems known as B. Conjecture B: "The increase in annual salary of the CEO per unit omitted variables and irrelevant variables. [4 marks] improvement in the firm's performance (as measured by the ROA) is higher B. Use distribution graphs to illustrate the explanations. [6 marks] for male executives than female executives, and the increase in the CEO's C. Is either of the two problems a small-sample problem? [3 marks] annual salary per additional year of age is higher for males than for females." Indicate which test statistic can be used to test this conjecture, writing clearly ii) Discuss the coefficient of determination RZ of an OLS regression model y = B, + the null and alternative hypotheses. B2xt + & as requested in the following questions: [6 marks] A. Write down the expression of the coefficient of determination as an explicit function only of: the Residual Sum of Squares (RSS) and Total Sum of C. Conjecture C: "The annual salary of a male CEO is higher than that of a female Squares (TSS). Note: the term only indicates that the RZ should be written as CEO, ceteris paribus (any other thing equal)." Using the same model written a function exclusively of the RSS, TSS and no other variable. [2 marks] in A., Indicate which test statistic can be used to test this conjecture, writing B. Write down the expression of the coefficient of determination as an explicit clearly the null and alternative hypotheses. function only of: the observations on the dependent variable ypt = 1, .... T, [3 marks] and the model's predictions or fitted values put = 1, ..., T. [4 marks] C. Provide two examples of situations in which it is not appropriate to use the RZ statistic to compare the fit of competing OLS regression models. Formally explain why the R cannot be used in those situations. [3 marks] D. Provide alternative statistics or tests that can be used to compare the fit of competing OLS regression models in the situations described in C. Write down the definitions (or expressions) of the alternative statistics or tests. [4 marks] iii) Suppose that a researcher has collected data for a cross-section of i = 1,2, .., N firms. Salary, denotes the annual salary of the CEO of firm i in thousands of pounds, Tenure, denotes experience of the CEO expressed in years, Age denotes the CEO's age, Gender, is equal to 1 if the CEO is a male (0 otherwise), ROA, denotes the return-on-assets of the firm in percentage points. All of the data correspond to the same given year , except ROA which is measured as an average over years , f-1 and f-2. (continued in next page) Write down a general model that, exploiting all of the above data, will allow you to conduct formal tests to assess the following three conjectures
