QUESTION 1

(i) Specify a simple linear regression model and explain the notation used. Derive the intercept and slope estimates using the method of ordinary least squares (OLS). (30 marks)

(ii) Outline the assumptions under which the OLS estimators derived in part (i) are the best  linear  unbiased  estimators  (BLUE).  What  is  the  difference  between  these assumptions and the classical linear model (CLM) assumptions? (10 marks)

(iii) What is multicollinearity and how does it affect the OLS estimators? Briefly discuss

possible ways in which researchers may improve the efficiency of these estimators.   (10 marks)

(iv) Using a sample of US firms (CEOSAL1.DTA), two researchers run a regression of CEOs’ salaries (lsalary) on three firm performance measures, namely annual sales (lsales), return on equity (roe), and stock return (ros), as well as a finance dummy variable (finance). lsalary and lsales are in log form while roe and ros are measured in percentage. finance is equal to one if the company operates in the financial sector and zero otherwise. Below is the output from this regression.

. reg lsalary lsales roe ros finance

Number of obs F(4, 204)    Prob > F

R-squared    Adj R-squared Root MSE

=

=

=

=

=

=

209 21.91 0.0000 0.3005 0.2868 .4783

Write the fitted  OLS  regression  line.  Explain  relevant  statistics and  interpret the coefficient estimates. (20 marks)

(v) Formulate the hypothesis that CEOs of financial firms earn 10% higher than CEOs of non-financial firms. Also, write the hypothesis that the elasticity of salary with respect to sales (i.e., the coefficient on lsales) is greater than 0.2. Using both the confidence intervals and appropriate statistics, test these hypotheses. Comment on the validity of your testing procedures. If you were to run the regression again, what would you do to improve your statistical inference? (15 marks)

(vi) The researchers in part (iv) wish to further improve their model specification. One researcher questions the inclusion of ros in the model given the limited impact of this variable on lsalary. The other researcher raises the concern that the current model does not allow for a possibility in which the impact of the three firm performance measures on CEO compensation may be conditional on the finance variable. She argues  that  because  financial  companies  are  highly  regulated  and  monitored, managerial  pay  is  potentially  more sensitive to firm  performance for those firms. Advise the researchers on how to address these concerns. Clearly write the regression model(s) and describe any testing procedures they should use . (15 marks)

SECTION B

Choose EITHER Question 2 OR Question 3

QUESTION 2

(i) Specify a simple (two-period) panel data model. Discuss alternative methods for estimating this model in detail. Outline the conditions under which these methods are valid. (30 marks)

(ii) Using data on US firms for the period 1971–2006 (cash.dta), a group of accounting and finance scholars investigate what determines firms’ cash policies. They regress cash holdings (CASH), measured as the ratio of cash balances to total assets, on five independent variables, namely (1) the market to book ratio (MTB), (2) firm size (SIZE), measured as the log of total assets, (3) cash flow (CFA), measured as the ratio of cash flow to total assets, (4) capital expenditures (CAPEX), measured as the ratio of capital expenditures to total assets, and (5) leverage (LEV), measured as the ratio of total debt to total assets. They first estimate their model as follows:

. reg CASH MTB SIZE CFA CAPEX LEV, robust Linear regression

Number of obs

F(5, 9125)

Prob > F

R-squared

Root MSE

=

=

=

=

=

9,131 228.00 0.0000 0.1972 .10197

What estimator do the scholars use? Interpret the regression results and examine whether the coefficient estimates are statistically significant . Do the scholars use an appropriate method to estimate the standard errors? Clearly explain why or why not. (15 marks)

(iii) The scholars re-estimate their cash holdings model using two methods: the pooled OLS  (POLS) and fixed  effects  (FE) estimators.  In  both  regressions, they cluster standard errors at the firm level. Columns (1) and (2) of the following table report the POLS and FE regression results, respectively.