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ECO-5006A: Introductory Econometrics

Take-Home Written Exercise 2

We are provided with data on a random sample of 302 companies from a particular sector

in New York (NY) and we are interested in how employee salary is affected by some company

characteristics. We have information on the following variables:

avgsal : average employee salary in $

sales : annual company sales in $

employ : number of employees in the company

north : =1 if company operates in North NY, =0 otherwise

south : =1 if company operates in South NY, =0 otherwise

Note that Central NY is the base group. We start the analysis by specifying the following

MLR model:

log(avgsali) = β0 + β1 log(salesi) + β3employi + β4employ2

i + ui

, i = 1, 2, . . . , 302

Estimating this by OLS, we obtain the following estimated results (with t-stats in square

brackets):

log(\avgsali) = 7.34

RSS = 35.649

where RSS is the Residuals Sum of Squares from this regression.

(a) Based on these results, interpret the estimated coefficient associated with log(sales) and

test for its statistical significance. In addition, interpret the estimated intercept.

[15 marks]

We now add dummy variables north and south, and estimating this model by OLS, we obtain

the following results (with t-stats in square brackets):

log(\avgsali) = 7.36

(b) Based on these results, interpret the estimated coefficients associated with variables north

and south and test whether the two variables have a joint significant effect on log(avgsal).

[25 marks]

(c) Is there statistical evidence of a quadratic relationship between log(avgsal) and the number

of employees in a company? In addition, holding the other variables constant, calculate

the approximate percentage change in average employee salary, if the number of employees

in a company changes by 10 employees, for (i) employ = 50 and (ii) employ = 150.

[30 marks]

TURN OVER

We now remove employees2

from the model and add log(sales) × employ, the interaction

term between log(sales) and employ. Estimating this model by OLS we obtain (with t-stats

in square brackets): (3)

(d) Based on these results, is there statistical evidence that the effect of the number of

employees on average employee salary depends on company sales? In addition, holding

the other variables constant, calculate the approximate percentage change in average

employee salary, if the number of employees in a company changes by 10 employees, for

(i) sales=$2,000,000 and (ii) sales=$2,000,000,000. [30 marks]

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