Econometrics Homework (Lab Course: Chapters 2, 3, 4)

Homework

Exercise 1

Question:

Data set CEOSAL2.RAW includes information about 177 CEOs, which can be used to explore the effect of corporate performance on the salary of CEOs. Check variable labels and know the meanings of the variables. Complete the following questions:

1. Estimate the regression model of annual salary with sales volume and market value as independent variables in which constant elasticity of each variable is specified. Present the estimation result.

2. If adding profits into the model in 1, could this variable be in logarithmic form? Do these corporate performance variables explain most of the variation in CEOs’ salaries?

3. Based on 2, add ceoten into the model and keep other conditions the same. What is the estimated percentage return if CEO tenure increases by one year?

4. Calculate the correlation coefficient between logarithmic market value and profits. Are they highly correlated? How it affects the OLS estimation?

5. Use partial regression to calculate the elasticity of market value to CEO’s salary by using a single regression model.

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Do.file document and results:

1. Import data : “CEOSAL2.DTA”

use "CEOSAL2.DTA", clear	

2. Describe the variables to know meanings of them

describe			

variable name	storage type	display format	variable label
salary	int	%9.0g	1990 compensation, $1000s
age	byte	%9.0g	in years
college	byte	%9.0g	=1 if attended college
grad	byte	%9.0g	=1 if attended graduate school
comten	byte	%9.0g	years with company
ceoten	byte	%9.0g	years as ceo with company
sales	float	%9.0g	1990 firm sales, millions
profits	int	%9.0g	1990 profits, millions
mktval	float	%9.0g	market value, end 1990, mills.
lsalary	float	%9.0g	log(salary)
lsales	float	%9.0g	log(sales)
lmktval	float	%9.0g	log(mktval)
comtensq	int	%9.0g	comten^2
ceotensq	int	%9.0g	ceoten^2
profmarg	float	%9.0g	profits as % of sales
e_lmktval	float	%9.0g	Residuals

3. Answer to 1.1

$log(salary)={\beta }_0+{\beta }_{1}log(sales)+{\beta }_{2}log(mktval)+u$

reg lsalary lsales lmktval
dis "log(salary)=" _b[_cons] "+" _b[lsales] "log(sales)+" _b[lmktval] "log(mktval)"

Source	SS	df	MS
Model	19.3365617	2	9.66828083	Number of obs = 177
Residual	45.3096514	174	.260400295	F(2, 174) = 37.13
Total	64.6462131	176	.367308029	Prob > F = 0.0000
				R-squared = 0.2991
				Adj R-squared = 0.2911
				Root MSE = .51029

lsalary	Coef.	Std. Err.	t	P>|t|	[95% Conf. Interval]
lsales	.1621283	.0396703	4.09	0.000	.0838315 .2404252
lmktval	.106708	.050124	2.13	0.035	.0077787 .2056372
_cons	4.620917	.2544083	18.16	0.000	4.118794 5.123041

$log(salary)=4.6209175+.16212831log(sales)+.10670798log(mktval)$

4. Answer to 1.2

First we need to know if it is appropriate to add profits into the model in 1 in logarithmic form.

sum profit   

Variable	Obs	Mean	Std. Dev.	Min	Max
profits	177	207.8305	404.4543	-463	2700

We can see the minimum of profit is negative.

count if profit < 0

count if profit < 0
9

We can see if we add profits into the model in 1 in logarithmic form, there will be nine missing value. Because there are nine negative observations in variable profit. Hence, we should not add profits into the model in 1 in logarithmic form, but in level form.

l o g ( s a l a r y ) = β 0 + β 1 l o g ( s a l e s ) + β 2 l o g ( m k t v a l ) + β 3 p r o f i t s + u log(salary)=\beta_0+\beta_1log(sales)+\beta_2log(mktval)+\beta_3profits+u log(salary)=β