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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
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]
END OF PAPER