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ECN6540 ECONOMETRIC METHODS – COURSEWORK 2021

The answers to the questions must be type-written. The preference is that symbols and equations should be inserted into the document using the equation editor in Word. Alternatively, they can be scanned and inserted as an image (providing it is clear and readable). Maximum words 1,500 excluding any Stata output and commands.

The coursework comprises two questions where the second is a short Stata assignment. Both questions 1 and 2 carry equal weight and the marks shown within each question indicate the weighting given to component sections.

YOU MUST USE A TURNITIN SUBMISSION TEMPLATE SEE INFORMATION ON BLACKBOARD UNDER ASSESSMENT INFORMATION/TURNITIN SUBMISSION.

PLEASE WRITE YOUR STUDENT REGISTRATION NUMBER IN THE SUBMISSION TITLE BOX.

ANSWER ALL QUESTIONS SET.



1.

Using data from the UK in 2009 the salary of 447 Chief Executive Officers (CEOs) was modelled as a double logarithmic function of firm profit, sales, a quadratic in CEO tenure (years with the firm) and a set of CEO age binary indicators, as shown in equation (1):

log(���������������������) = ���0 + ���1log(���������������������) + ���2log(������������������) + ���3���������������������

3

+ ���4������������������2 + ��������������������� + ������

���

���=1

(eq. 1) where ��� is the unit of observation (CEO) and log denotes the natural logarithm. Age binary indicators are defined as follows: ���������1 = 1 if the CEO is aged between 45-54, 0 otherwise; ���������2 = 1 if the CEO is aged between 55-64, 0 otherwise; and ���������3 = 1 if the CEO is aged between 65 or over, 0 otherwise. The reference category is aged below 45. The following Stata output shows the estimates

(where tenure_sq denotes ������������������2).

regress lsalary lprofit lsales tenure tenure_sq age1 age2 age3


Source | SS df MS

Number of obs

=

447

-------------+----------------------------------

F(7, 439)

=

Model | 48.7304908

Prob > F

=

Residual |

R-squared

=

-------------+----------------------------------

Adj R-squared

=

Total | 180.917437

Root MSE

=

.54873

------------------------------------------------------------------------------

lsalary | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

lprofit

|

.0283458

.007029

4.03

0.000

.0145312

.0421604

lsales

|

.3156325

.0352641

8.95

0.000

.246325

.38494

tenure

|

.0297118

.0078598

3.78

0.000

.0142643

.0451594

tenure_sq

|

-.0005955

.0002093

-2.84

0.005

-.0010069

-.000184

age1

|

.3817208

.1670604

2.28

0.023

.0533833

.7100584

age2

|

.4344553

.1624551

2.67

0.008

.1151689

.7537417

age3

|

.5185316

.1793046

2.89

0.004

.1661295

.8709336

_cons

|

3.860184

.3485608

11.07

0.000

3.175129

4.54524

------------------------------------------------------------------------------


sum lsalary lprofit lsales tenure


Variable | Obs Mean Std. Dev. Min Max

-------------+---------------------------------------------------------


a.

b.

Interpret the results.

Draw a diagram in salary and year space to roughly plot the shape and relative position of the tenure function based upon the above output. Explain whether the shape of the function concurs with the

findings of age?

[10 marks]

[7 marks]


c.

d.

e.

f.

g.

h.

i.

j.

Calculate the value of tenure at which salary is maximised.

For the continuous explanatory variables calculate the slope and elasticity, based at the sample mean.

Calculate the value of the RSS and the degrees of freedom associated with the ESS, RSS and TSS.

Test whether the parameters on the explanatory variables are jointly statistically significant at the 5% level.

Showing your calculation in full find the adjusted R-squared.

Re-write the regression model shown in equation (1) to allow for differential profit and sales elasticities with respect to age.

Explain in detail how you would test whether there are differential profits and sales elasticities across the different age groups.

The initial model (equation 1) is now re-estimated changing the functional form to a quadratic in age as shown in equation (2):

log(���������������������) = ���0 + ���1log(���������������������) + ���2log(������������������) + ���3���������������������

+ ���4������������������2 + ���5������������ + ���6���������2 + ������

��� ���

(eq. 2)

The following Stata output shows the estimates. Which model is preferred (equation 1) or (equation 2), explain your answer?

[7 marks]

[10 marks]

[4 marks]

[7 marks]

[10 marks]

[8 marks]

[25 marks]

[12 marks]